Warm-Up

  Think of three examples of waves.   What do waves have in common?   What, if anything, do waves carry from one place

to another?

WAVES Physics

Waves

  If you can only remember one thing…

  The source of all waves is something that vibrates.

Waves transmit ENERGY from one place to another.

Simple Harmonic Motion

  Simple Harmonic Motion (SHM) – Back and forth oscillatory motion.

  Ex: Pendulums, Springs   Motion looks like a sine curve.

Parts of a Wave

TROUGH

CREST

Wave Description

  Crest – high point on a wave   Trough – low point on a wave   Amplitude (A) – the distance from the midpoint to the

crest   Wavelength (λ)– the distance from the top of one

crest to the top of the next one (or between successive identical parts of the wave)

  Frequency (f)– number of vibrations an object makes per second, units are in Hertz (Hz = 1 cycle/second)

  Period (T) – number of seconds it takes to go through one vibration

Frequency and Period

  Frequency (f) and period (T) are reciprocals of each other.

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f =1T

T =1f

  Ex: If the frequency of a wave is 4 Hz, what is its period?

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T =1f

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T =14sec

Wave Motion

  Most of the information around us gets to us in some form of wave.

  Sound is energy that travels to our ears in the form of one kind of wave.

  Light is energy that comes to our eyes in the form of a different kind of wave.

  The signals that reach our radios and TVs also travel as waves.

Wave Motion

 When energy is transferred by a wave from a vibrating source to a distant receiver, there is no transfer of matter between the two points!

 The energy transferred from a vibrating source to a receiver is carried by a disturbance in a medium, not by matter moving from one place to another within the medium.

Shallow Water Wave

A circular water wave in a still pond moves out from the center in an

expanding circle.

Wave Speed

  The speed of a wave depends on the medium through which it travels.

  Whatever the medium, the speed, wavelength, and frequency of the wave are related

Wave speed = wavelength X frequency

[m/s] = [m] x [Hz]

  Sound waves move at speeds of about 340 m/s in air and four times faster in water.

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v = λ × f

Checking for Understanding:

  Complete the following table:

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v = λ × f

Transverse Waves

  Transverse Waves – the motion of the medium is at right angles to the direction in which the wave travels

  Examples: stretched strings in musical instruments, waves on surfaces of liquids, radio waves, light waves, and s-waves (earthquakes)

Example Problem

  The water waves below are traveling with a speed of 2 m/s and splashing periodically against the Wilbert's perch. Each adjacent crest is 4 meters apart and splashes Wilbert’s feet upon reaching his perch. How much time passes between each successive drenching?

Longitudinal Waves

  Longitudinal Waves – particles move along the direction of the wave

  Examples: sound waves and p-waves (earthquakes)

Warm-Up

1.  What is the difference between a transverse wave and a longitudinal wave?

2.  Wave troughs hit the tip of an anchored boat every 6 seconds. If the waves are traveling at 5 m/s, what is the distance between each trough?

3.  Explain what is transferred as a stadium of people does “the wave.”

4.  How fast does sound travel in air?

Interference

  Interference Pattern – arrangement of places where wave effects are increased, decreased, or neutralized

Interference

  Constructive Interference (reinforcement) – the crest of one wave overlaps the crest of another, their individual effects add together producing an increased amplitude

  Destructive Interference (cancellation) – the crest of one wave overlaps the trough of another, their individual effects are reduced

Standing Waves

  Standing Wave – certain parts of the wave remain stationary, when the incident wave and reflected wave meet

  Nodes – part of the standing wave which does not move and has no amplitude (at equilibrium)

  Antinodes – position on a standing wave which has the largest amplitude

Warm-Up

Warm-Up

1.  The lowest pitch that the average human can hear has a frequency of 20.0 Hz. If sound with this frequency travels through air with a speed of 330 m/s, what is its wavelength?

2.  The world’s largest guitar, which was built by high school students in Indiana, has strings that are 9.0 m long. The fundamental vibration that can be induced on each string has a wavelength equal to twice the string’s length. If the wave speed in a string is 9.0 x 102 m/s, what is the frequency of vibration?

SOUND Physics

Sound

  All sounds originate in the vibrations of material objects.

  Sound is a longitudinal wave.   A pulse of compressed air is called a compression.   A pulse of low-pressure air is called a rarefaction.

Compression Rarefaction

Sound

  Sound travels in solids, liquids, and gases.   The speed of sound differs in different materials.   In generally, sound is transmitted faster in liquids

than in gases, and still faster in solids.   Sound cannot travel in a vacuum.   The speed of sound in dry air = 330-340 m/s.

Loudness

  Loudness is a psychological sensation sensed in the brain, and it differs for different people.

  Loudness varies as the logarithm of intensity (wave energy).   (ex: An increase from 10 dB to 20 dB

means the sound is 10 times louder).

  The unit of intensity for sound is the decibel (dB), named after Alexander Graham Bell.

Natural Frequency & Resonance

  When an object is disturbed, it vibrates at its own special set of frequencies, which make a certain sound.

  The natural frequency of an object depends on the elasticity and shape of the object.   When an object vibrates at its natural frequency, it uses the

least amount of energy.

  Resonance - When the forced vibration on an object matches its natural frequency, an increase in amplitude occurs.

Natural Frequency & Resonance

Interference and Beats

  When constructive interference occurs with sound waves, the listener hears a louder sound.

  When destructive interference occurs, the listener hears a fainter sound or no sound at all.  Noise-cancelling headphones

  When two tones of slightly different frequency are sounded together, a regular fluctuation in the loudness of the combined sounds is heard.

  The periodic variation in the loudness of sound is called beats.

Interference

Warm-Up

1.  What happens when an object is forced to vibrate at its natural frequency? What is this called?

2.  What type of interference is produced when the rarefaction of one sound wave overlaps the compression of another?

3.  T or F: Sound can travel through a vacuum. 4.  What happens to the frequency of a sound wave

as the sound wave approaches an observer?

The Doppler Effect

  Doppler Effect – The apparent change in frequency of a wave due to the motion of the source or the observer.

  As a wave source approaches, an observer encounters waves at a higher frequency. As the wave source moves away, an observer encounters waves with a lower frequency.

  Ex: Ambulance siren passing you.

Doppler Effect Formula

  f = actual frequency [Hz]   f’ = apparent frequency [Hz]   v = wave speed [m/s] (for sound this is 340 m/s)   vo = observer speed [m/s]   vs = source speed €

f '= fv ± vo( )v ± vs( )

Doppler Possibilities

**Source moving away from observer (+) Source moving toward observer (-)

**Observer moving towards source (+) Observer moving away from source (-)

Doppler Example 1

  A police car, whose siren has frequency 1080 Hz, is traveling at 30 m/s. We are traveling at 50 m/s away from the police as he chases us. Find the frequency which we hear.

Doppler Example 2

  Sitting on the beach at Coney Island one afternoon, Sunny finds herself beneath the flight path of the airplanes leaving JFK. What frequency will Sunny hear as a jet, whose engines emit sound at a frequency of 1000 Hz, flies toward her at a speed of 100 m/s?

Warm-Up

1.

2

PS4 Solutions

1.  852.5 Hz 2.  188 Hz 3.  A. 92.3 Hz

B. 78.7 Hz 4.  5.3 m/s 5.  89.5 Hz 6.  813 Hz

Warm-Up

1.  An explosion occurs 680 km away. How long does it take that sound to reach you?

2.  If you double the frequency of a vibrating object, it’s period ________.

3.  If you wanted to produce sound with a wavelength in air equal to the length of a 3 m room, what would its frequency be?

Waves in Strings

  The frequency with which a string vibrates depends upon the number of half wavelengths, the wave speed, and the length of the string.

  If n=1, the frequency is called the fundamental frequency. It is the lowest frequency of vibration that is fixed at both ends.

  Multiples of the fundamental frequency are called overtones.

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f =nv2L

n = # of half wavelengths L = length of string

Example 1

  Zeke plucks a C on his guitar string, which vibrates with a fundamental frequency of 261 Hz. The wave travels down the string with a speed of 400 m/s.

  a) What is the length of the guitar string?   b) Would Zeke need longer or shorter strings to

play the fundamental frequency for higher notes?

Waves in Pipes

  Waves in pipes that are open in both ends behave much like strings.

  Antinodes always form at the end of open pipes:   Nodes form at closed ends:

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f =nv4L

n = # quarter λ’s L = length of string

Example 2

  An orchestra tunes up for the big concert by playing an A, which resounds with a fundamental frequency of 440 Hz. Find the first and second overtones of this note. Assume the instruments act like pipes, which are open at both ends.

Example 3

  In his physics lab, Bob finds that he can take a long glass tube and fill it with water, using the air space at the top to simulate a pipe closed at one end. If Bob holds a tuning fork, which vibrates with a fundamental frequency of 440 Hz, over the mouth of the pipe, how long is the air column if it vibrates at the same frequency?

Beats

  If two different frequencies sound simultaneously, the wavelengths will differ, and the crests and troughs of each wave will overlap in a way that causes variations in loudness.

  There will be moments of reinforcement and moments of cancellation as the wave patterns interact. The resulting sound is a series of beats.

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fB = f2 − f1