Waves and Sound

• Waves– Are disturbances that move through an empty space

or through medium (atoms and molecules)– Waves transfer energy without transferring matter.– Particles of medium move in simple harmonic motion

Mechanical: Through a medium

Electromagnetic: Through empty space

• Mechanical wave:– Caused by a disturbed medium and move by action

reaction of particles– ex: water wave, sound

• A medium is matter particles like gas (ex. air), liquid (ex. Water), and solid (ex. earth)

Two types of mechanical waves that require a medium

Transverse Wave

Longitudinal Wave

Electromagnetic wave:• Move through empty space (no medium)• Created by moving electrons• Ex. radio waves, microwaves, light

Through empty space

Types Electromagnetic Waves

• In order to start and transmit a wave, a source of disturbance (vibration) and a disturbed medium or electron are required.

• Mechanical caused by vibrating particles

• Electromagnetic by vibrating electrons

Section 2: Types of Mechanical Waves

Transverse Longitudinal

Transverse Wave:• Wave particles move perpendicular to the

direction the wave travels• Ex. vibrating string of a musical instrument

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dir

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Direction of travel

• Crest- highest point on a transverse wave• Trough- lowest point on a transverse

wave• Equilibrium position- center around

which simple harmonic motion occurs• Amplitude- from the equilibrium position

to the crest or trough

Longitudinal Wave:• Particles vibrate parallel to the direction

the wave travels• ex. sound wave

Direction of travel

Particles vibrate parallel to the direction of travel

Parts of a Longitudinal Wave:

• Compression- point where the particles are closest together

• Rarefaction- point where the particles are furthest apart

Compression

Rarefaction

Intro Questions

1. What do all waves transfer?2. What don’t waves transfer?3. What starts a wave?

Pick between the following choices and answer this correctly:

4. Sound is a (mechanical or electromagnetic) (transverse or longitudinal) wave.

Section 3: Relationship between Wavelength,

Frequency and Wave Speed

Mechanical wave velocity

• The velocity of the wave depends on the material it is traveling through.

• For a mechanical wave, which needs a medium, the more elastic the medium the faster the wave.

• Slower Fastest• Gas liquid solid

Electromagnetic Wave Velocity

• The velocity of the wave depends on the material it is traveling through.

• For a electromagnetic wave, which can travel without a medium like in space, the more elastic the medium gets in the way and slows down the wave.

• Slower Fastest• No medium (space) gas liquid solid

• velocity ( v ): speed of the wave.– unit: m/s (meter/second)

• frequency ( f ): vibrations per second of the wave– unit: Hz (hertz)

• wavelength ( ג ): length of one wave pulse– unit: m (meter)

Lets revisit our old equation

What is the velocity of an object that moves 25 meters in 3 seconds?

V= ___d

t

Lets revisit our old equation

What is the velocity of an object that moves 25 meters in 3 seconds?

V= ___d

t

Now lets look at the new equation you can use as well.

V= ___d

t

oldnew

Example what is the velocity of a wave that has a frequency of 3Hz and a wavelength of 5m?

Now lets look at the new equation you can use as well

V= ___d

t

oldnew

Now lets look at the new equation you can use as well

V= ___d

t

oldnew

Now lets look at the new equation you can use as well

V= ___d

t

oldnew

Now lets look at the new equation you can use as well

V= ___d

t

oldnew

Relationship between frequency and wavelength when wave velocity is the same.• Wavelength and frequency are inversely

related• As frequency goes up the wavelength gets

shorter (assuming no change in velocity)

Click for animation

Period (T) vs. Frequency (f)

• Period (T) – seconds for one cycle– (unit s)

• Frequency (f) – cycles for one second – (unit Hz)

• If you know one you can solve for the other

Example 1Wave Math

The frequency of a wave is 560 Hz. What is its period?

The frequency of a wave is 560 Hz. What is its period?

Example 2Wave Math

A girl floats in the ocean and watches 12 wave crests pass her in 46 s. Calculate the wave: a) frequency b) period

A girl floats in the ocean and watches 12 wave crests pass her in 46 s. Calculate the wave: a) frequency b) period

Example 3Wave Math

The period of a wave is 0.044s. How many cycles will the energy source make in 22s?

cycles

second

The period of a wave is 0.044s. How many cycles will the energy source make in 22s?

Example 4Wave Math

A distance of 0.33 m separates a wave crest from the adjacent trough, and the vertical distance from the top of a crest to the bottom of a trough is 0.24m. A. What is the wavelength?B. What is the amplitude?

0.33m

0.24m

Example 4Wave Math

A distance of 0.33 m separates a wave crest from the adjacent trough, and the vertical distance from the top of a crest to the bottom of a trough is 0.24m. A. What is the wavelength?B. What is the amplitude?

0.33m

0.66m

Example 4Wave Math

A distance of 0.33 m separates a wave crest from the adjacent trough, and the vertical distance from the top of a crest to the bottom of a trough is 0.24m. A. What is the wavelength?B. What is the amplitude?

0.24m 0.12m

Example 5Wave Math

What is the speed of a 256 Hz sound with a wavelength of 1.35 m?

Example 5Wave Math

What is the speed of a 256 Hz sound with a wavelength of 1.35 m?

Example 6Wave Math

You dip your finger into a pan of water 14 times in 11s, producing wave crests separated by 0.16 m.

A. What is the frequency?B. What is the period?C. What is the velocity?

Example 6Wave Math

You dip your finger into a pan of water 14 times in 11s, producing wave crests separated by 0.16 m.

A. what is the frequencyB. What is the periodC. Velocity

Section 4: The Pendulum

• Pendulum- a weight on a string that moves in simple harmonic motion (swings back and forth).

• Movement from a to c and back to a is one complete cycle or vibration

accelerating decelerating

This is the equilibrium position.

• Simple harmonic motion- vibration about an equilibrium position– Constant back and forth motion over the

same path.– 15º is the maximum angle for a pendulum to

have simple harmonic motion where our equations work

• Masses do not effect the period in simple harmonic motion.

• What effects the period:• L – length of the string• g – acceleration due to gravity

Example 7

A tall tree sways back and forth in the breeze with a frequency of 2Hz. What is the period of this tree?

Example 7

A tall tree sways back and forth in the breeze with a frequency of 2Hz. What is the period of this tree?

Hypnotist Paulbar the great swings his watch from a 0.20 m chain in front of a subjects eyes. What is the period of swing of the watch.

Example 8

Hypnotist Paulbar the great swings his watch from a 0.20 m chain in front of a subjects eyes. What is the period of swing of the watch.

Example 8

A spider swings slightly in the breeze from a silk thread that is 0.09 m in length. What is the period of the simple harmonic motion?

Example 9

A spider swings slightly in the breeze from a silk thread that is 0.09 m in length. What is the period of the simple harmonic motion?

Example 9

If a pendulum is shortened, does the period increase or decrease? What about its frequency?

Example 10

If a pendulum is shortened, does the period increase or decrease? What about its frequency?

Example 10

Period decreases

Frequency increases

• Finish section 4 of the worksheets and turn in your packet today when you are done.

• Work on something else quietly while you wait for everyone to complete their work

Section 5: Wave Interactions

• Reflection• Refraction• Diffraction• Interference

Reflection:• The turning back of a wave at the

boundary of a new medium (bouncing back)

• Ex: light off a mirror, or sound echo

• Incident wave- incoming

• Waves reflected off a fixed boundary are inverted.– A fixed boundary is one not allowed to move

• Waves reflected off a flexible boundary are upright.– A flexible boundary is allowed to move

Law of Reflection:• Angle of reflection of a wave equals angle

of incidence• θr = θi

• Normal line – line perpendicular to surface being reflected off of.

θr

θiNormal line

Example 11

• Draw the reflected wave, labeling angles of incidence, reflection, and the normal line

35º

Wave front:• Portion of a medium’s surface in which

particles are in phase• Particles in phase are in the same stage of

their vibration.

Refraction:• the bending of a wave path as it enters a

new medium obliquely (indirectly)• caused by difference in speed of the new

medium• fast to slow – bends toward the normal line• slow to fast – bends away from normal

Refraction

• Light travels slower in water

• Draw the refracted wave, labeling the normal line, angle of incidence, and angle of refraction.

SlowFast

θi

θr

Normal line

Example 13

Diffraction:• Spreading of waves

around edges or through an opening of a boundary

• Is greatest when size of opening is smaller than wavelength

Principle of Superposition: • Displacement of a medium by two or more

waves is the algebraic sum of the displacements of the waves alone

Interference:• Result of the superposition of two

or more waves• constructive- (crest meets crest

or trough meets trough) amplitudes add

• destructive – (crest meets trough) amplitudes subtract

• Only temporary as paths cross

Constructive interference

Only temporary as paths cross

Destructive interference

Only temporary as paths cross

Constructive and destructive interference in two sine waves

Example 14 (finish off the drawings)

Before During After

Constructive interference

Destructive interference

Antinodal lineLines of constructive interference

Nodal lineLines of destructive interference

Wave Fronts Interfering

Standing wave:• created by waves with same

frequency, wavelength, and amplitude traveling in opposite directions and interfering.

• consists of nodes (o amplitude) and antinodes (max amplitude)

• produced by certain frequencies

Standing Waves Being Produced

NodeAntinode

Section 6: Sound

• Sound waves are produced by a vibrating object

• Sound waves are longitudinal mechanical waves.

Sound Frequency:

• Determines pitch

• 20 – 20,000 Hz are audible to an average person

• Less than 20 Hz are infrasonic

• Greater than 20,000 Hz are ultrasonic

Click for Frequency Modulator

Echolocation and Sonar

• Sonar is simply making use of an echo.

• An echo is used to locate an object.

• When an animal or machine makes a noise, it sends sound waves into the environment around it.

• Those waves bounce off nearby objects, and some of them reflect back to the object that made the noise.

• Whales, Dolphins, Bats, and many more organisms use sound for locating prey and predators

Less than 20 Hz- Infrasonic

Sound Velocity

• Largely depends on medium elasticity

• Solids>liquids>gasses

• Then depends on temperature– Faster at higher temperatures– Air (at 0ºC) v = 331 m/s and +/-

0.6 m/s per ºC

Generally between phases vsolids > vliquids > vgases

Sound Velocity Equations

v = 331 + 0.6 Tc

v = d/t

v = fλ

Interesting sound facts• Sound travels 15 times faster in the steel from a

railroad track.

• Sound travels 4 times faster in water

• At sea level, the speed of sound is 340 m/s or 760 mi/hr. This is called mach 1.

The speed of sound will be the same for all frequencies under the same conditions.

– Wavelength and frequency are inversely related

– As frequency goes up the wavelength gets shorter

What is the speed of sound at room temperature (22ºC)

Example 15

What is the speed of sound at room temperature (22ºC)

How many seconds will it take to hear an echo if you yell toward a mountain 110 m away on a day when air temperature is -6.0 ºC?

Example 16

How many seconds will it take to hear an echo if you yell toward a mountain 110 m away on a day when air temperature is -6.0 ºC?

Example 17

If sound travels at 340 m/s, how many seconds will it take thunder to travel 1609m?

Example 17

If sound travels at 340 m/s, how many seconds will it take thunder to travel 1609m?

Example 18

A sonar echo takes 3.1s to go to a submarine and back to the ship. If sound travels at 1400m/s in water, how far away is the submarine?

Example 18

A sonar echo takes 3.1s to go to a submarine and back to the ship. If sound travels at 1400m/s in water, how far away is the submarine?

Example 19

On a day when air temperature is 11ºC, you use a whistle to call your dog. If the wavelength of the sound produced is 0.015m, what is the frequency? Could you hear the whistle?

Example 19

On a day when air temperature is 11ºC, you use a whistle to call your dog. If the wavelength of the sound produced is 0.015m, what is the frequency? Could you hear the whistle?

Section 7: The Doppler Effect

Doppler Effect

• Change in pitch caused by relative motion of source and observer

• Pitch increases as sound and observer approach (and vice versa)

Doppler Effect Problems

• Frequency rises when its coming closer and lowers when moving away.

Example 20

Sitting on a beach at Coney Island one afternoon, Sunny finds herself beneath the flight path of airplanes leaving Kennedy Airport. What frequency will Sunny hear as a jet, whose engines emit sound at a frequency of 1000 Hz, flies towards her at a speed of 100.0 m/s? (use 340 m/s as the speed of sound)

Example 20

Sitting on a beach at Coney Island one afternoon, Sunny finds herself beneath the flight path of airplanes leaving Kennedy Airport. What frequency will Sunny hear as a jet, whose engines emit sound at a frequency of 1000 Hz, flies towards her at a speed of 100.0 m/s? (use 340 m/s as the speed of sound)

Example 21

Sitting on a beach at Coney Island one afternoon, Sunny finds herself beneath the flight path of airplanes leaving Kennedy Airport. What frequency will Sunny hear as a jet, whose engines emit sound at a frequency of 1000 Hz, flies away from her at a speed of 100.0 m/s? (use 340 m/s as the speed of sound)

Example 21

Sitting on a beach at Coney Island one afternoon, Sunny finds herself beneath the flight path of airplanes leaving Kennedy Airport. What frequency will Sunny hear as a jet, whose engines emit sound at a frequency of 1000 Hz, flies away from her at a speed of 100.0 m/s? (use 340 m/s as the speed of sound)

Example 22

A sparrow chases a crow with a speed of 4.0 m/s, while chirping at a frequency of 850.0 Hz. What frequency of sound does the crow hear as he flies away from the sparrow at a speed of 3.0 m/s? (use 340 m/s as the speed of sound)

Example 22

A sparrow chases a crow with a speed of 4.0 m/s, while chirping at a frequency of 850.0 Hz. What frequency of sound does the crow hear as he flies away from the sparrow at a speed of 3.0 m/s? (use 340 m/s as the speed of sound)

Intro

You are chasing after your parent’s car because you forgot your lunch in it. You are running at a swift 4.0 m/s and your parent is going 12 m/s. It is a cold 5.0° C today and your voice is producing a frequency of 460 Hz. Your parent’s car is squealing a bit and producing a frequency of 760 Hz.

1. What frequency would your parent hear you at if he/she could?

2. What frequency do you hear your parent’s car at?

You are chasing after your parent’s car because you forgot your lunch in it. You are running at a swift 4.0 m/s and your parent is going 12 m/s. It is a cold 5.0° C today and your voice is producing a frequency of 460 Hz. Your parent’s car is squealing a bit and producing a frequency of 760 Hz.

1. What frequency would your parent hear you at if he/she could?

You are chasing after your parent’s car because you forgot your lunch in it. You are running at a swift 4.0 m/s and your parent is going 12 m/s. It is a cold 5.0° C today and your voice is producing a frequency of 460 Hz. Your parent’s car is squealing a bit and producing a frequency of 760 Hz.

2. What frequency do you hear your parent’s car at?

CW/HW

• Section 7 of Worksheet Packet

Section 8: Intensity and Perceived Sound

• The property of sound waves associated with loudness is amplitude

• The property associated with pitch is frequency

Section 9: Resonance and Music

Resonance in Music

• Forced Vibration- The vibration of an object that is made to vibrate by another vibrating object.

• Sympathetic vibrations- secondary vibrations caused by forced vibration of a first object.

• Sounding board- part of an instrument forced into vibration to amplify sound

Example of creating forced vibrations to make a sound louder

• Sounding board of a musical instrument.• Example: guitar makes a strings vibrations

resonate

Resonance:

• Also called sympathetic vibrations

• Dramatic increase in the amplitude of a wave when the frequency of an applied force matches the natural frequency of the object.

Resonance can be dangerous

• Wind caused the Tacoma Narrows suspension bridge to vibrate at its natural frequency.

• The amplitude of the vibrations caused too much strain on the bridge until it collapsed.

Difference between music and noise

• Noise- a random mixture of a large number of sound frequencies

• Music- Sound frequency or mixture of frequencies with a pattern

Percussion Instrument:

• Musical sound produced by striking the object

• Frequency depends on the mass of the object.

• To raise the pitch- decrease the mass of the object.

• Ex- drums, xylophone, bells

Stringed Instrument• Musical sound produced by

plucking or blowing strings• Frequency depends on

four factors• To raise pitch

– 1. decrease diameter of string

– 2. increase tension– 3 decrease length– 4. decrease density of string

material• Examples: guitar, violin

Wind Instrument

• Musical sound produced by vibrating air column

• Frequency depends mainly on length of air column

• To raise pitch- decrease the size of the air column

• Examples- oboe, flute

• Standing Waves are formed in the instrument due to vibrations

• When the natural frequency is hit the sound amplifies

Open Ended Wind Column Instrument

• Must be nodes at both ends

Closed Ended Wind Column Instrument

• There is an antinode at the closed end.

• Count standing waves by including the return trip.

• Acoustics- field of study related to sound

• Acoustic designers try to maximize the quality of sound reaching the audience– Control the size, shape, and material used– They try and control the reflection

• Reverberation- If a reflected sound wave reaches the ear within 0.1 seconds of the initial sound, then it seems to the person that the sound is prolonged.

• Echoes- A perceived second sound that arrives after the first has died out.– Echoes occur when a reflected sound wave

reaches the ear more than 0.1 seconds after the original sound wave was heard.

Two types of reflection with sound

• Interference causes beats – Beats occur due to constructive and

destructive interference between sounds with close but not exact frequencies.