Waves and Sound

AP Physics 1

What is a wave

A WAVE is a vibration or disturbance in space.

A MEDIUM is the substance that all MECHANICAL WAVES travel through and need to have in order to move. Ex. Sound

Periodic waves repetitive patterns occur as a result of simple

harmonic motion.

Think back to events that can create simple harmonic motion…

Two types of Waves

Transverse Wave - A fixed point will move perpendicular with the wave motion.

The second type of wave is called Transverse.

Wave parts(recall demo for simple harmonic motion )- crest, trough, wavelength, amplitude, frequency, period

Two types of WavesThe first type of wave is called Longitudinal.

Longitudinal Wave - A fixed point will move parallel with the wave motion

2 areasCompression- an area of high molecular density and pressureRarefaction - an area of low molecular density and pressure

Although sound is a longitudinal wave, it may be graphed as pressure-time and the sinusoidal characteristic is evident:

Wave components definitions: Wavelength: λ,

Frequency : f,

Period: T = 1/f,

Speed of Propagation: v=f λ .

Amplitude (A) -

Parts of Waves 2

Crest

Trough

Wavelength

Amplitude

Crest

Trough

Wavelength

Amplitude

Wave Speed

You can find the speed of a wave by multiplying the wave’s wavelength in meters by the frequency (cycles per second). Since a “cycle” is not a standard unit this gives you meters/second.

ExampleA harmonic wave is traveling along a rope. It is observed that the

oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along a rope in 10.0 s . What is the wavelength?

33.1

425.0

/425.010

425.0

33.130

40

sec

fv

smt

xv

Hzcycles

f

wave 0.0319 m/s

Waves on a String

Speed is related to tension in the string: The greater the tension, the faster the wave speed.

Speed is related to mass per unit length of the string: The thicker the string, the slower the wave propagates.

Fixed End ReflectionConsider a rope – one end free to move, the other end fixed. a pulse is

introduced at the free end (incident pulse) and travels toward the fixed end. When the pulse reaches the fixed end, it reflects and is inverted.

Other notable characteristics of the reflected pulse include: The speed of the reflected pulse is the same as the speed of the incident

pulse. The wavelength of the reflected pulse is the same as the wavelength of the

incident pulse. The amplitude of the reflected pulse is less than the amplitude of the

incident pulse. (in the real world. in physics land they would be the same)

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Fixed End Animation

Free End Reflection

Consider a rope – both ends are free. the reflected pulse is not inverted.

15

Free End Animation

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Change in Medium

Our third boundary condition is when the medium of a wave changes.

Think of a thin rope attached to a thin rope. The point where the two ropes are attached is the boundary.

At this point, a wave pulse will transfer from one medium to another.

What will happen here?

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Change in Medium

In this situation part of the wave is reflected, and part of the wave is transmitted.

Part of the wave energy is transferred to the more dense medium, and part is reflected.

The transmitted pulse is upright, while the reflected pulse is inverted.

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Change in Medium

The speed and wavelength of the reflected wave remain the same, but the amplitude decreases.

The speed, wavelength, and amplitude of the transmitted pulse are all smaller than in the incident pulse.

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Change in Medium Animation

Superposition - Two waves in the same medium interfere. the result is a new wave that is the sum of the original waves Constructive Interference–The superposition of

two equal wave pulses resulting in a combined wave of larger amplitude than its components.

Destructive Interference

Destructive Interference–The superposition of two wave pulses with equal but opposite amplitude.

Wave Phase o Comparing the location of two waves in the same medium.

o Points on one wave can also be in phase.

o Two crests are in phase. o A crest and a trough are

1800 out of phase. o If two waves are 1800 out

of phase, they will destructively interfere.

o If they are in phase, they will constructively interfere.

Standing Waves Standing Waves–Wave

pattern that results when two waves of the same frequency, wavelength and amplitude travel in opposite directions and interfere.

Node–point in a standing wave that always undergoes complete destructive interference.

Antinode–point in a standing wave, halfway between two nodes, at which the largest amplitude occurs

More Standing Waves

Reflection

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Refraction

Waves traveling from the deep end to the shallow end can be seen to refract (i.e., bend), decrease wavelength (the wavefronts get closer together), and slow down (they take a longer time to travel the same distance).

When traveling from deep water to shallow water, the waves are seen to bend in such a manner that they seem to be traveling more perpendicular to the surface.

If traveling from shallow water to deep water, the waves bend in the opposite direction.

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Diffraction Water waves have the ability to travel around corners, around obstacles and through openings. This ability is most obvious for water waves with longer wavelengths.

Diffraction can be demonstrated by placing small barriers and obstacles in a ripple tank and observing the path of the water waves as they encounter the obstacles.

The waves are seen to pass around the barrier into the regions behind it; subsequently the water behind the barrier is disturbed.

The amount of diffraction (the sharpness of the bending) increases with increasing wavelength and decreases with decreasing wavelength.

In fact, when the wavelength of the waves is smaller than the obstacle, no noticeable diffraction occurs

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Sound is a mechanical wave.

Sound is a Pressure Wave Because of the longitudinal motion of the air

particles, there are regions in the air where the air particles are compressed together and other regions where the air particles are spread apart. These regions are known as  compressions and rarefactions respectively. The compressions are regions of high air pressure while the rarefactions are regions of low air pressure.

Sound WavesSound Waves are a common type of standing wave as they

are caused by RESONANCE.

Resonance – when a FORCED vibration matches an object’s natural frequency thus producing vibration, sound, or even damage.

One example of this involves shattering a wine glass by hitting a musical note that is on the same frequency as the natural frequency of the glass. (Natural frequency depends on the size, shape, and composition of the object in question.) Because the frequencies resonate, or are in sync with one another, maximum energy transfer is possible.

Infrasonic

Infrasonic – sounds that are below 20 Hz Elephants, whales, alligators and other creatures

use infrasonics to communicate over hundreds of miles. (low frequency requires a larger amount of medium to be moved making it harder to dampen)

The 1883 eruption of Krakatoa produced an infrasonic wave that circled the earth 7 times and was picked up on barometers worldwide.

Earth’s Hum – sensitive seismometers constantly pick up a sound of 3-7 mHz. Source unknown

Ultrasonic Ultrasonic – frequencies above 20,000 Hz Bats, cats, dogs, and rodents use this for

communication. An ultrasound measures how these waves are

reflected back at different speeds as the medium through which they travel changes. The computer takes this info and creates a picture model.

Sound WavesThe production of sound involves setting up a wave in air. To set up

a CONTINUOUS sound you will need to set a standing wave pattern.

Three LARGE CLASSES of instruments Stringed - standing wave is set up in a tightly stretched string Percussion - standing wave is produced by the vibration of solid

objects Wind - standing wave is set up in a column of air that is either

OPEN or CLOSED

Factors that influence the speed of sound are density of solids or liquid, and TEMPERATURE

The Speed of Sound

vsolids > vliquids > vgases

v = 331 m/s + (0.6 m/s/C)•T

Resonance and Standing Waves

Nearly all objects, when hit or struck or plucked or strummed or somehow disturbed, will vibrate. If you drop a meter stick or pencil on the floor, it will begin to vibrate. If you pluck a guitar string, it will begin to vibrate. If you blow over the top of a pop bottle, the air inside will vibrate. When each of these objects vibrates, they tend to vibrate at a particular frequency or a set of frequencies. The frequency or frequencies at which an object tends to vibrate with when hit, struck, plucked, strummed or somehow disturbed is known as the natural frequency of the object. If the amplitudes of the vibrations are large enough and if natural frequency is within the human frequency range, then the vibrating object will produce sound waves that are audible.

Forced Vibration

 The tendency of one object to force another adjoining or interconnected object into vibrational motion is referred to as a forced vibration.

 This is an example of resonance - when one object vibrating at the same natural frequency of a second object forces that second object into vibrational motion.

Closed PipesHave an antinode at one end and a node at the other. Each sound

you hear will occur when an antinode appears at the top of the pipe. What is the SMALLEST length of pipe you can have to hear a sound?

You get your first sound or encounter your first antinode when the length of the actual pipe is equal to a quarter of a wavelength.

This FIRST SOUND is called the FUNDAMENTAL FREQUENCY or the FIRST HARMONIC.

Closed Pipes - HarmonicsHarmonics are

MULTIPLES of the fundamental frequency.

In a closed pipe, you have a NODE at the 2nd harmonic position, therefore NOSOUND is produced

Closed Pipes - HarmonicsIn a closed pipe you have an ANTINODE at the 3rd

harmonic position, therefore SOUND is produced.

CONCLUSION: Sounds in CLOSED pipes are produced ONLY at ODD HARMONICS!

Open PipesOPEN PIPES- have an antinode on BOTH ends of the

tube. What is the SMALLEST length of pipe you can have to hear a sound?

You will get your FIRST sound when the length of the pipe equals one-half of awavelength.

Open Pipes - HarmonicsSince harmonics are MULTIPLES of the

fundamental, the second harmonic of an “open pipe” will be ONE WAVELENGTH.

The picture above is the SECOND harmonic or the FIRST OVERTONE.

Open pipes - HarmonicsAnother half of a wavelength would ALSO produce an

antinode on BOTH ends. In fact, no matter how many halves you add you will always have an antinode on the ends

The picture above is the THIRD harmonic or the SECOND OVERTONE.

CONCLUSION: Sounds in OPEN pipes are produced at ALL HARMONICS!

ExampleThe speed of sound waves in air is found to be 340

m/s. Determine the fundamental frequency (1st harmonic) of an open-end air column which has a length of 67.5 cm.

f

f

lfv

)675.0(2340

2

251.85 HZ

ExampleThe windpipe of a typical whooping crane is about

1.525-m long. What is the lowest resonant frequency of this pipe assuming it is a pipe closed at one end? Assume a temperature of 37°C.

f

fv

lfv

)525.1(4

4

331)]37)(6.0[( 353.2 m/s

57.90 Hz

The Doppler Effect

The is the apparent change in frequency due to moving sound source or moving observer.

As the source and/or observer move toward each other, perceived frequency increase.

As the source and/or observer move away from each other, perceived frequency decreases.

OR

Shock Waves and Sonic Booms The circular lines represent

compressional wavefronts of the sound waves. Notice that these circles are bunched up at the front of the aircraft. This phenomenon is known as a shock wave.

Mach An object traveling at the

speed of sound is said to be traveling at mach 1 (331m/s or 740 mph)

Traveling at mach 2 is traveling twice as fast as sound.

Fastest manned airplane is the SR-71 Blackbird – Mach 3.2

Fastest manned aircraft x-15 Mach 6.7

Fastest unmanned aircraft is x-43 Mach 9.8 – operated 11 seconds before crashing into the ocean

The Doppler Effect and Astronomy: Electromagnetic radiation emitted by stars in a distant

galaxy would appear to be shifted downward in frequency (Red Shift) if the star is rotating in its cluster in a direction which is away from the Earth. On the other hand, there is an upward shift in frequency (Blue Shift) of such observed radiation if the star is rotating in a direction that is towards the Earth.

Doppler Effect Animation