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Radar

Radar was developed secretly for military use by several nations, before and during World War II.The term was coined in 1940 by the United States Navy as an acronym for RAdio Detection And Ranging. It entered English and other languages as a common noun, losing all capitalization.

Radar uses radio waves to determine the range, angle, or velocity of objects.

transverse-wave
*
em-wave-gif
*
EM waves can be of many different wavelengths.
Longer wavelengths we perceive as orange and red
Shorter wavelengths are towards the blue end of the spectrum

Fields are at right-angles to each other

They travel through vacuum (empty space) at the speed of light

c  =  speed of light
c  =  3 x 108 m/s       =   186,282 miles/second

So all parts of the EM spectrum – radio, light, Wi-Fi, X-rays,
are all made of exactly the same thing! The only thing different among them? wavelength and frequency!

colors-different-wavelengths-prism

Our eyes can only see a tiny amount of the EM spectrum.
There are longer and shorter waves as well.

Gamma rays Spectrum Properties NASA

Is  used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain.

A radar system consists of:

transmitter producing electromagnetic radio waves

a receiving antenna (often the same antenna is used for transmitting and receiving)

a receiver and processor to determine properties of the object(s)

Radio waves from the transmitter reflect off the object and return to the receiver

This gives info about the object’s location and speed.

Uses

air and terrestrial traffic control

radar astronomy

air-defence systems / antimissile systems

tba

marine radars to locate landmarks and other ships

Commercial marine radar antenna

aircraft anticollision systems

radar by Marshall Brain

outer space surveillance and rendezvous systems

meteorological (weather) precipitation monitoring

Weather radar

flight control systems

guided missile target locating systems

ground-penetrating radar for geological observation

Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

6.MS-PS4-1. Use diagrams of a simple wave to explain that (a) a wave has a repeating pattern with a specific amplitude, frequency, and wavelength, and (b) the amplitude of a wave is related to the energy of the wave.

HS-PS4-1. Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling within various media. Recognize that electromagnetic waves can travel through empty space (without a medium) as compared to mechanical waves that require a medium.

HS-PS4-5. Communicate technical information about how some technological devices use the principles of wave behavior and wave interactions with matter to transmit and capture information and energy. Clarification Statements:
• Emphasis is on qualitative information and descriptions.
• Examples of technological devices could include solar cells capturing light and
converting it to electricity, medical imaging, and communications technology.

Massachusetts Science and Technology/Engineering Curriculum Framework (2006)

6. Electromagnetic Radiation Central Concept: Oscillating electric or magnetic fields can generate electromagnetic waves over a wide spectrum. 6.1 Recognize that electromagnetic waves are transverse waves and travel at the speed of light through a vacuum. 6.2 Describe the electromagnetic spectrum in terms of frequency and wavelength, and identify the locations of radio waves, microwaves, infrared radiation, visible light (red, orange, yellow, green, blue, indigo, and violet), ultraviolet rays, x-rays, and gamma rays on the spectrum.

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Vapor cones and mach cones

A vapor cone, also known as shock collar or shock egg, is a visible cloud of condensed water which can sometimes form around an object moving at high speed through moist air, for example an aircraft flying at transonic speeds.

FA-18 Hornet breaking sound barrier July 1999 US Navy

When the localized air pressure around the object drops, so does the air temperature. If the temperature drops below the saturation temperature a cloud forms.

prandtl glauert vapor cloud Mach
In the case of aircraft, the cloud is caused by supersonic expansion fans decreasing the air pressure, density and temperature below the dew point. Then pressure, density and temperature suddenly increase across the stern shock wave associated with a return to subsonic flow behind the aircraft. Since the local Mach number is not uniform over the aircraft, parts of the aircraft may be supersonic while others remain subsonic — a flight regime called transonic flight.


 

A vapor cone is caused by the formation of so-called ‘Prandtl–Meyer’ expansion fans, which temporarily decrease the air pressure, density and temperature below the air’s dew point. It is not the same thing as the Mach Cone (which is an invisible pressure front), but the two often occur in tandem, allowing us to pretend that we have just seen the sound barrier broken. In this incredible clip of a Boeing F/A-18 Hornet flying at a height of 25 feet, you can see both the Vapor Cone and evidence of the Mach Cone on the surface of the water…

http://physicsfootnotes.com/vapor-cone-versus-mach-cone/

 

Sonar and ultrasound

Sonar (SOund Navigation And Ranging)

The use of sound to navigate, communicate with, or detect objects – on or under the surface of the water – such as another vessel.

Old Navy Sub sonar GIF

Active sonar uses a sound transmitter and a receiver.

Active sonar creates a pulse of sound, often called a “ping”, and then listens for reflections (echo) of the pulse

Active sonar Wikipedia

Natural sonar

whales

dolphins

echolocation of a dolphin wikipedia

bats

Ultrasound

Medical ultrasound – a diagnostic imaging technique using ultrasound.

Used to see internal body structures such as tendons, muscles, joints, vessels and internal organs.

The practice of examining pregnant women using ultrasound is called obstetric ultrasound.

Ultrasound is sound waves with frequencies which are higher than those audible to humans (>20,000 Hz).

Ultrasonic images also known as sonograms are made by sending pulses of ultrasound into tissue using a probe.

The sound echoes off the tissue; with different tissues reflecting varying degrees of sound. These echoes are recorded and displayed as an image to the operator.

Medical ultrasound (Wikipedia)

Ultrasound human heart 4 chambers Wikipedia

“Amniocentesis is a prenatal test in which a small amount of amniotic fluid is removed from the sac surrounding the fetus for testing. The sample of amniotic fluid (less than one ounce) is removed through a fine needle inserted into the uterus through the abdomen, under ultrasound guidance. The fluid is then sent to a laboratory for analysis. Different tests can be performed on a sample of amniotic fluid, depending on the genetic risk and indication for the test.”

Amniocentesis: WebMD

Amniocentesis image006

 

 

Doppler effect

The Doppler effect

Named after Austrian physicist Christian Doppler who proposed it in 1842.

You hear the high pitch of an approaching ambulance’s siren – and then notice that its pitch drops as it passes you. That’s the Doppler effect.

Listen to the Doppler effect! A passing car beeps its horn

Doppler effect Acela express train

Doppler effect racetrack

The Big Bang Theory – The Doppler Effect

Doppler effect YouTube example 1

Doppler effect YouTube example 2

sound frequency increases during the approach,
is identical as it passes by,
and decreases during the recession.
(Adapted from Wikipedia.)

Watch the spacing of the sound waves, when the car is at rest, and when it is in motion. How does motion change the spacing of the waves?

http://www.acs.psu.edu/drussell/Demos/doppler/doppler.html

doppler-effect-car-frequency

Step 1: Staying at rest

In the center is a stationary sound source.
It produces sound waves.
The wavefronts propagate symmetrically away from the source,
at a constant speed

stationary-sound-source-produces-sound-waves-doppler

 

Step 2: Now the source is moving quickly.

Since the source is moving, the centre of each new wavefront
is slightly displaced to the right.

As a result, the wave-fronts begin to bunch up in front of,
and spread further apart behind, the source.

So an observer in front of the source will hear a higher frequency.

doppler-effect-source-moving-right-mach-0-7

We can see this in water: Doppler effect of water flow around a swan

doppler-effect-of-water-flow-around-a-swan

 

Doppler effect applet

Doppler applet (with sound)

Doppler effect and sonic booms

MCAS problems

By the end of our unit on waves we should be able to do MCAS Physics exam: sample wave problems

 

Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

HS-PS4-1. Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling within various media. Recognize that electromagnetic waves can travel through empty space (without a medium) as compared to mechanical waves that require a medium

SAT subject test in Physics: Waves and optics

• General wave properties, such as wave speed, frequency, wavelength, superposition, standing wave diffraction, and Doppler effect
• Reflection and refraction, such as Snell’s law and changes in wavelength and speed
• Ray optics, such as image formation using pinholes, mirrors, and lenses
• Physical optics, such as single-slit diffraction, double-slit interference, polarization, and color

MCAS wave problems

MCAS Physics exam: Example Problems

buzzer-near-pendulum-doppler-mcas-2011

MCAS 2011

Which of the following describes and explains what the observer hears as the buzzer moves away from him?

A. a lower-pitched buzz than the buzzer’s normal sound because the sound waves are arriving less frequently
B. a higher-pitched buzz than the buzzer’s normal sound because the sound waves are arriving more frequently
C. a lower-pitched buzz than the buzzer’s normal sound because the velocity of the sound waves is reduced by the velocity of the swinging buzzer
D. a higher-pitched buzz than the buzzer’s normal sound because the velocity of the sound waves is increased by the velocity of the swinging buzzer

#25, MCAS 2011

longitudinal air wave in tube MCAS 2011.PNG

#32. Essay question, MCAS 2011

A large anchor is being lifted into a boat with metal sides. As the anchor leaves the water it
hits the side of the boat, making loud sounds and making waves on the surface of the water.

a. Describe the motions of the sound waves and the water waves.
b. Draw a diagram for each of the waves you described in part (a). Be sure to label each
diagram.
c. Describe how the wavelength is measured for the water waves

#35. Which of the following observations demonstrates that visible light waves are
electromagnetic and not mechanical?

A. Sunlight can pass through gas.
B. Sunlight can pass through solids.
C. Sunlight can pass through liquids.
D. Sunlight can pass through a vacuum.

#37, MCAS 2011
Which of the following statements best explains why lightning is seen before thunder is heard?

A. Electromagnetic waves travel faster than mechanical waves in air.
B. Electromagnetic waves have a higher frequency than mechanical waves.
C. Electromagnetic waves experience less interference than mechanical waves.
D. Electromagnetic waves form faster than mechanical waves during a thunderstorm.

#3, MCAS 2011
In a large room, a sound wave traveling from a violin produces a tone with a frequency of 264 Hz. The speed of sound in the room is 340 m/s.  What is the wavelength of the sound wave from the violin?

A. 0.004 m      B. 0.80 m      C. 1.3 m    D. 2.6 m

MCAS 2012

2. When music plays through the speaker, the speaker rapidly moves back and forth in the cabinet. Which of the following conclusions is best supported by this observation?

A. Sound travels only in air.
B. Sound is a transverse wave.
C. Sound is a longitudinal wave.
D. Sound travels at the speed of light

4. Which of the following statements best describes a difference between mechanical waves and electromagnetic waves?
A. Mechanical waves can produce colored light, while electromagnetic waves cannot.
B. Mechanical waves can travel in any direction, while electromagnetic waves travel only in one direction.
C. Mechanical waves travel only through a medium, while EM waves can also travel through a vacuum.
D. Mechanical waves travel only at the speed of light, while electromagnetic waves can travel at many different speeds.

6. A student is sitting on the edge of a swimming pool. The student repeatedly dips his foot in and out of the pool, making waves that move across the water. The student dips his foot slowly at first and then does it faster, each time to the same depth. Which of the following properties of the waves increases as the student dips his foot faster?

A. frequency
B. period
C. velocity
D. wavelength

21. A rope is stretched horizontally between two students. One of the students shakes an end of the rope up and down. Which of the following terms best describes the type of wave that is produced?

A. electromagnetic
B. longitudinal
C. rotational
D. transverse

#26. MCAS 2012

mcas-2012-represent-an-em-wave

#29. Student X and student Y are receiving sound waves from a stationary source. The sound waves have a frequency of 10 kHz. Student X is stationary and student Y is traveling toward the source of the sound waves.
Which of the following statements describes what will happen as student Y moves?

A. Student X will receive sound waves with a frequency higher than 10 kHz.B. Student X will receive sound waves with a frequency lower than 10 kHz.
C. Student Y will receive sound waves with a frequency higher than 10 kHz.
D. Student Y will receive sound waves with a frequency lower than 10 kHz.

#37 Two waves traveling in the same medium are shown below.

mcas-2012-comparing-waves

Which of the following correctly compares the two waves?
A. Wave X has half the amplitude of wave Y.
B. Wave X has twice the amplitude of wave Y.
C. Wave X has a lower frequency and longer wavelength than wave Y.
D. Wave X has a higher frequency and shorter wavelength than wave Y

#42 In which of the following media do sound waves most likely travel the fastest?
A. crude oil
B. distilled water
C. solid steel
D. warm air

MCAS 2013

#2. A student is shaking one end of a small rug with a ball on top of it. The wave that is produced travels through the rug and moves the ball upward, as shown in the diagram below

shake-rug-waves-mcas-2013

#6. A person is driving north in a car at a constant speed. A police officer is
driving south toward him at a constant speed. The police officer uses a radar
unit to measure the speed of the person’s car. The radar unit sends out waves of
a certain frequency toward the person’s car. The waves reflect off the person’s car and travel back to the radar unit in the police car. What happens to the frequency of the waves detected by the radar unit?
A. The frequency is lower as the person’s car approaches.
B. The frequency is higher as the person’s car approaches.
C. The frequency remains the same but with increased energy as the person’s car approaches.
D. The frequency remains the same but with decreased energy as the person’s car approaches.

#22. Which of the following properties makes a light wave different from all mechanical waves?
A. A light wave slows down in a vacuum.
B. A light wave is able to transmit energy.
C. A light wave exists as a transverse wave.
D. A light wave can travel without a medium

#25. Which of the following observed properties of a wave is changed by the Doppler effect?
A. amplitude
B. direction
C. frequency
D. speed

#28. The diagram below shows two students making a wave with a coiled spring

mcas-2103-spring-waves-on-tabletop

MCAS 2014

#2. Waves rock a boat in the middle of a pond. The boat moves up and down 10 times in 20 seconds. What is the period of the waves?
A. 0.5 s       B. 2 s     C. 10 s     D. 20 s

#16. A sound wave with a frequency of 1,700 Hz is traveling through air at a speed of 340 m/s. What is the wavelength of this sound wave?
A. 0.2 m     B. 5.0 m    C. 2,040 m      D. 57,800 m

#19. Sunscreen protects skin by absorbing harmful ultraviolet radiation from the Sun. Ultraviolet radiation has which of the following properties?
A. a shorter wavelength than x-rays
B. a lower frequency than radio waves
C. a higher frequency than visible light
D. a longer wavelength than microwaves

#23. ESSAY. Waves can be classified as either electromagnetic or mechanical.
a. Describe two differences between electromagnetic and mechanical waves.
b. Give two examples of electromagnetic waves.
c. Give two examples of mechanical waves.

#26. A wave with a wavelength of 3.2 m is generated in a pond. The frequency of the wave is 0.60 Hz. What is the speed of this wave?
A. 0.19 m/s
B. 1.9 m/s
C. 3.8 m/s
D. 5.3 m/s

#30. The diagram below shows a representation of two different waves

2-spring-waves-transverse-longitudinal-mcas-2014

MCAS 2015

14. A train driver blows the train’s horn as it moves away from a station. Which of the following statements describes how the sound of the horn heard by an observer standing at the station platform differs from the sound heard by the train driver?
A. The observer hears the sound as having a greater velocity.
B. The observer hears the sound as having a lower frequency.
C. The observer hears the sound as having a greater amplitude.
D. The observer hears the sound as having a shorter wavelength

#17. A windsurfer moves at 5 m/s while staying on the crest of a wave, as shown below.

mcas-2015-windsurfer-waves

#29. A seismic wave called a P-wave travels through the solid part of Earth. In a P-wave, the solid particles of Earth move parallel to the direction the P-wave travels. P-waves are which of the following types of waves?
A. electromagnetic
B. longitudinal
C. torsional
D. transverse

#38.  At a given temperature, a longitudinal mechanical wave will travel fastest through which of the following?
A. a gas
B. a liquid
C. a solid
D. a vacuum

#45. Essay and Drawing! A floating object moves up and down 15 times in 60 s because of ocean waves.
a. Calculate the period of the ocean waves. Show your calculations and include units in
your answer.
b. Calculate the frequency of the ocean waves. Show your calculations and include units in
your answer.

An additional wave property must be known in order to calculate the velocity of the ocean
waves.
c. In your Student Answer Booklet, identify this additional wave property and draw a wave
diagram showing how the property can be measured.
d. Describe what will happen to the object if the amplitude of the ocean waves increases and all other wave characteristics stay the same

**

Textbook p.393, #18.

How does increasing the wavelength of a rope by 50 % decreases its frequency by 33 %.

The relation between frequency and wavelength is

fλ=v

Then

f1λf2λ2

If ff, then f1.50f

λλ× f1fλ× f1.500.67λ1

The new wavelength is 67 % of the original (33 % less than the original).

Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

HS-PS4-1. Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling within various media. Recognize that electromagnetic waves can travel through empty space (without a medium) as compared to mechanical waves that require a medium

SAT subject test in Physics: Waves and optics

• General wave properties, such as wave speed, frequency, wavelength, superposition, standing wave diffraction, and Doppler effect
• Reflection and refraction, such as Snell’s law and changes in wavelength and speed
• Ray optics, such as image formation using pinholes, mirrors, and lenses
• Physical optics, such as single-slit diffraction, double-slit interference, polarization, and color

Waves in 2 dimensions

Waves in 2-dimensions

Glencoe Physics, Chapter 14.
glencoe-physics-book-cover

Throw a stone into water: observe the circular crests and troughs

Waves propagate in 2 dimensions:

along the X-axis, and Y-axis, simultaneously.

a wavefront represents the crest of a wave in 2 dimensions

2-dimensional waves always travel perpendicular to their wavefronts

wave’s direction is represented by a ray

Here, water waves, or light waves, hit a curved surface

The wavefronts reflect to a point, called the focus.

Refraction of 2-D waves

Refraction is the change in direction of wave propagation due to a change in its transmission medium.

Often seen with light.

Seen with water waves, when they move from deep water into shallow water.

Here light waves refrac as they move from one medium into another (from air into diamond)

In this simplified case, the light waves (or water waves) are all parallel to each other.

Here we see the same thing, but now the rays of light are more realistic.

They emanate from a source, so they are circular, not parallel.

Yet when the rays hit the water, they are approximately parallel, so the result is the same.

snells-law-wavefronts

Snell’s law at PhysicsClassroom.com

Water waves can be refracted

Animation: Wiley Refraction

Animation GCSE Light and water refraction

Here we see water waves changing direction, as they enter shallower waters.

water-wave-refraction-into-a-bay

From a presentation by Luo Yanjie.

From a presentation by Luo Yanjie.

 

Details on the cause of refraction (PhysicsClassroom.Com)

 

Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

HS-PS4-1. Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling within various media. Recognize that electromagnetic waves can travel through empty space (without a medium) as compared to mechanical waves that require a medium

SAT subject test in Physics: Waves and optics

• General wave properties, such as wave speed, frequency, wavelength, superposition, standing wave diffraction, and Doppler effect
• Reflection and refraction, such as Snell’s law and changes in wavelength and speed
• Ray optics, such as image formation using pinholes, mirrors, and lenses
• Physical optics, such as single-slit diffraction, double-slit interference, polarization, and color

Measuring data with smartphone apps

On Physics Central Tamela Maciel writes:

That smartphone you carry around in your pocket all day is a pretty versatile lab assistant. It is packed with internal sensors that measure everything from acceleration to sound volume to magnetic field strength. But I’ll wager most people don’t realize what their phones can actually do. Apps like SensorLog (iOS) or AndroSensor (Android) display and record raw data from the phone’s movement, any background noises, and even the number of satellites in the neighborhood. Watching this data stream across my screen, I’m reminded just how powerful a computer my phone really is. Wrapped into one, the smartphone is an accelerometer, compass, microphone, magnetometer, photon detector, and a gyroscope. Many phones can even measure things like temperature and air pressure.

http://physicsbuzz.physicscentral.com/2015/01/your-smartphone-can-do-physics.html

Apps

Physics Toolbox Sensor Suite (Google Android)

Physics Toolbox Sensor Suite (Apple iOS)

physics-toolbox-sensor-suite

Useful for STEM education, academia, and industry, this app uses device sensor inputs to collect, record, and export data in comma separated value (csv) format through a shareable .csv file. Data can be plotted against elapsed time on a graph or displayed digitally. Users can export the data for further analysis in a spreadsheet or plotting tool. See http://www.vieyrasoftware.net for a variety of usage ideas

SENSORS
(1) G-Force Meter – ratio of Fn/Fg (x, y, z and/or total)
(2) Linear Accelerometer – acceleration (x, y, and/or z)
(3) Gyroscope – radial velocity (x, y, and/or z)
(4) Barometer – atmospheric pressure
(5) Roller Coaster – G-Force Meter, Linear Accelerometer, Gyroscope, and Barometer
(6) Hygrometer – relative humidity
(7) Thermometer – temperature
(8) Proximeter – periodic motion and timer (timer and pendulum modes)
(9) Ruler – distance between two points
(10) Magnetometer – magnetic field intensity (x, y, z and/or total)
(11) Compass – magnetic field direction and bubble level
(12) GPS – latitude, longitude, altitude, speed, direction, number of satellites
(13) Inclinometer – azimuth, roll, pitch
(14) Light Meter – light intensity
(15) Sound Meter – sound intensity
(16) Tone Detector – frequency and musical tone
(17) Oscilloscope – wave shape and relative amplitude

__________________________________

PDF Labs to use with smartphone apps

https://mobilescience.wikispaces.com/Labs

EnglishIntroduction EspañolIntroducción
  1. Introduction to the accelerometer: Measurement of g.
  2. Frequency of Sound – Measure the frequency of sound.
  3. Magnetic field strength measurements.
  4. Time measurements with sound: Coefficient of Restitution.
  5. Introduction to photo gate timing using an external photo-resistor.
  6. Direct measurement of g using the sound of a falling object.
  7. Pendulum measurement of the acceleration of gravity using the accelerometer.
  8. Simple harmonic motion: Spring coefficient and damping.
  9. Inclined plane measurements using photo gates.
  10. Doppler shift – Measure the Doppler shift in the frequency of sound.
  1. Introducción a la acelerómetro: Medición de g.
  2. Frecuencia de sonido – Medir la frecuencia del sonido.
  3. Medidas de fuerza del campo magnético.
  4. Las medidas del tiempo con el sonido: coeficiente de restitución.
  5. Introducción a medidas de temporización con fotopuerta utilizando un foto-resistencia externa.
  6. La medición directa de g utilizando el sonido de un objeto cayendo.
  7. Medición del péndulo de la aceleración de la gravedad utilizando el acelerómetro.
  8. Movimiento armónico simple: Coeficiente de resorte y amortiguación.
  9. Mediciones de movimiento en el plano inclinado utilizando las fotopuertas.
  10. Desplazamiento Doppler – Medir el desplazamiento Doppler en la frecuencia del sonido.

https://mobilescience.wikispaces.com/Labs

Simple Harmonic Motion, and measuring Period

Smartphone Physics in the Park

Here’s a simple physics experiment you can do at your local park.
By swinging on a swing and collecting a bit of data, you can measure the length of the swing – without ever pulling out a ruler.

1. To get started, download the free SPARKvue app (or another data logger app like SensorLog or AndroSensor). Open it up and have a play.
By clicking on the measurement you want to track and then clicking on ‘Show’, you will see an graph window open with a green play button in the corner.
Click the play button and the phone will start tracking acceleration over time.
To stop recording, click the play button again.
Save your data using the share icon above the graph.

2. Find a swing.

3. Fix your phone to the swing chain with tape – or hold it really still against your chest in portrait orientation with the screen facing your body.
Since I was a bit lazy, I opted for the latter option but this makes the final data a bit messier with all the inevitable extra movement.
You want portrait orientation in order to measure the acceleration along the direction of the swing chains.
This will tell us how the centripetal acceleration from the tension in the chains changes as you swing.

4. Start swinging and recording the Y-axis acceleration, without moving your legs or twisting your body. Collect data for about 20 seconds.

5. Stop recording and have a look at your lovely sinusoidal graph.
You could try to do the next step directly from this graph.
I wanted a bigger plot, so I saved the raw data and copied it into Excel.

Here are the first 20 seconds of my swing.
Plotting the centripetal (Y-axis) acceleration against time.
You can immediately see the sine wave pattern of the swing,
and the fact that the height of the peaks is decreasing over time.
This is because all pendulums have a bit of friction and gradually come to a halt.
Keep in mind that this plot shows the change in acceleration, not velocity or position.

Acceleration of a swing, as measured along the chain of a swing. Data collected with SPARKvue and graphed in Excel. Credit: author, Tamela Maciel

6. Measure the period of the swing from the graph.

Direction of total velocity and acceleration for a simple pendulum.
Credit: Ruryk via Wikimedia Commons

To make sense of the peaks and troughs:
think about the point mid-swing when your speed is highest.
This is when you’re closest to the ground, zooming through the swing’s resting point.
It is at this point that the force or tension along the swing chain is highest, corresponding to a maximum peak on the graph.

The minimum peaks correspond to when you are at the highest point in the swing,
and you briefly come to a stop before zooming back down the other way.
Check out The Physics Classroom site for some handy diagrams of pendulum acceleration parallel and perpendicular to the string.

Once we know what the peaks represent,
we can see that the time between two peaks is half a cycle (period).
Therefore the time between every other peak is one period.

For slightly more accuracy, I counted out the time between 5 periods (shown on the graph)
and then divided by five to get an average period of 2.65 seconds per swing.

simple pendulum has a period that depends only on its length, l,
and the constant acceleration due to gravity, g:

I measured T = 2.65 s and know that g = 9.8 m/s/s,
so I can solve for l, the length of the swing.
I get l = 1.74 meters or 5.7 feet.

This is a reasonable value, based on my local swing set, but of course I could always double check with a ruler.

Now a few caveats: my swing and my body are not a simple pendulum, which assumes a point mass on the end of a weightless string.
I have legs and arms that stick out away from my center of mass, and the chains of the swing definitely do have mass.
So this simple period equation is not quite correct for the swing (instead I should think about the physics of the physical pendulum).
But as a first approximation, the period equation gives a pretty reasonable answer.

http://physicsbuzz.physicscentral.com/2015/01/your-smartphone-can-do-physics.html

By the way , here are comments on the above graph:

Claim: “Your graph is wrong. You write at the peaks, where the acceleration is highest, that the velocity is highest and the mid-swing-point. That is wrong. There is also a turning point with lowest velocity. The highest velocity and the mid-swing-point is where the acceleration is 0.”

Response #1

Remember, the phone is only recording the y-component of the total acceleration. At the end points the where the acceleration, a, is at maximum, but is at right angles to the chains so the y-component is zero.
This coincides with the velocity reaching zero as well.
At the mid-point where the velocity reaches maximum, the x-component of the acceleration is zero and the y-component reaches its maximum.
There is no point where the total acceleration reaches zero, only the x-component.

Response #2

My phone was measuring only the y-component of the acceleration, which from the way I held it, was only along the direction of the chains.
The maximum acceleration or force along the chains happens at the mid-point of the swing.
The minimum acceleration along the chains happens at the turning point.
So the graph is correct for the y-component acceleration.
But it would be interesting to repeat the experiment measuring the acceleration in the x-component, where the graph would look somewhat different.

Other experiments to explore

Morelessons from Vieyra software

http://www.vieyrasoftware.net/browse-lessons

Smartphones in science teaching

http://www.science-on-stage.de/page/display/en/7/7/678/istage-2-smartphones-im-naturwissenschaftlichen-unterricht1//

Mobile sensor apps for learning physics: A Google Plus community

https://plus.google.com/communities/117493961647466126964

Article: Turn Your Smartphone into a Science Laboratory

http://static.nsta.org/files/tst1509_32.pdf

Using smartphone apps to take physics day to the next level

https://quantumprogress.wordpress.com/2012/05/24/using-smartphone-apps-to-take-physics-day-to-the-next-level/

Placing the smartphone onto a record, playing on a turntable
To study angular motion

Smartphone app contest
http://physicsday.usu.edu/Information/ContestInfo/smartphone.asp

Many more ideas https://mobilescience.wikispaces.com/Ideas

Physics Toolbox Apps by Vieyra Software  http://www.vieyrasoftware.net/browse-lessons

Belmont University Summer Science Camp
Physics with Phones, Dr. Scott Hawley  http://hedges.belmont.edu/~shawley/PhonePhysics.pdf

References

Familiarizing Students with the Basics of a Smartphone’s Internal Sensors
Colleen Lanz Countryman, Phys. Teach. 52, 557 (2014)
http://dx.doi.org/10.1119/1.4902204
http://scitation.aip.org/content/aapt/journal/tpt/52/9/10.1119/1.4902204
Full text of article, in PDF format

http://scitation.aip.org/content/aapt/journal/tpt/52/3/10.1119/1.4865529

http://scitation.aip.org/content/aapt/journal/tpt/52/5/10.1119/1.4872422

http://iopscience.iop.org/0143-0807/35/4/045013/article

http://arxiv.org/pdf/1406.3867.pdf

http://scitation.aip.org/content/aapt/journal/tpt/52/8/10.1119/1.4897595