waves and sound

Waves and Sound

Intro

A. Pick up your notes and worksheet packetsB. Write the following questions on a blank piece of paper

(don’t answer yet)1. What is the difference between a

mechanical and electromagnetic wave?

2. What is the difference between a transverse and

longitudinal wave?3. What do all waves transfer?4. What don’t waves transfer?

Section 1: Intro to Waves

• Waves– Are disturbances that move through an empty space

or through medium (material)– 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• SOL= 3.0 x 10 8 m/s

Through empty space

Types Electromagnetic Waves

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

• Mechanical caused by vibrating particles– Like seen here

• Electromagnetic by vibrating electrons

Damping:

• A decrease in the amplitude of a wave

• Caused by energy loss or the spreading out of the wave over a larger area.

• Wave pulse is a single wave disturbance

• Wave train (continuous wave) - is a series of pulses at intervals

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

Pe

rpen

dic

ula

r to

th

e

dir

ecti

on

of

tra

vel

Direction of travel

Parts of a transverse wave

Crest

Trough

Equilibrium Position

Wavelength (ג)

Wavelength (ג)

Wavelength (ג)

amplitude

amplitude

• 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

• 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

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

Relationship between frequency and wavelength.

•Wavelength and frequency are inversely related

•As frequency goes up the wavelength gets shorter (assuming no change in velocity)

Click for animation

http://www.micro.magnet.fsu.edu/primer/java/wavebasics/index.html

http://www.micro.magnet.fsu.edu/primer/java/wavebasics/index.html

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


0.33m

0.66m

Example 4Wave Math


0.24m 0.12m

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

Assignment to work on:

CP

• Worksheet Packet Section 3

Honors

• Worksheet Packet Section 3

• Book Problems 4,5,6 pg 486-487

Pendulum Lab day: Your into is to read over your lab; I will ask you if there are any questions soon

Equilibrium Position

Amplitude (A)

Length (L)

Pendulum Lab day

One complete cycle

Intro after pendulum labAll labs are due today:

Turn them in on my desk

1. Your pendulum makes 5 complete cycles in 10 seconds.

a. What is the pendulums frequency?b. What is the pendulums period?

2. What is the definition of frequency (can be in equation form)

3. When you increase the length of the pendulum string, what happens to frequency?

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

Click here to interact with a pendulum

http://phet.colorado.edu/sims/pendulum-lab/pendulum-lab_en.html



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

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

• 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.

• Which two of these particles would be in phase?

Example 12

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

Normal Line

θi

θr

slow

Fast medium

Example 13

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

SlowFast

• 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

Show what you know

1. Refraction happens when waves –

a) Turn back at a boundary

b) Enter a new medium at an angle.

c) Go through an opening.

d) Are superpositioned.

2. This diagram shows which wave interaction?

a) Reflection

b) Refraction

c) Diffraction

d) Interference

3. Constructive interference occurs when-

a) Crest meets crest

b) Trough meets trough

c) Amplitudes add up

d) All of these

4. A line along which the medium does not vibrate is called a

a) Nodal line

b) Antinodal line

c) Construction

5. Standing waves are produced by waves of equal ________ traveling in opposite directions.

a) Wavelength

b) Frequency

c) Amplitude

d) All of the above

Intro Questions1. An echo bouncing off a nearby wall tends to

________________ back toward the source. 2. A pendulum requires 3 seconds to make one back and

forth motion. Calculate the pendulum’s frequency?3. Steam is rising from a cup of hot tea. What type of

thermal energy transfer is occurring? (conduction, convection, or radiation)

4. What type of interference would occur when these waves meet?

5. A water wave has a speed of 5m/s and the distance between each crest is 2.0m. What is the frequency of the water wave?

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

Uses of ultrasonic waves

More than 20,000 Hz- Ultrasonic waves

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- Subsonic or Infrasonic Sound

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 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?

Intro1. A 25,000Hz dog whistle can be heard by a dog but not by humans

because the frequency is in the ______________ range.

2. An elephant can hear below 20 Hz. This is the _________ range.

3. The range we can hear is between _____ and _______ and we call this range ______________.

4. Which of the following will sound travel fastest in?a) a swimming pool

b) a steel bridgec) a vacuumd) warm air

5. Sound wave A has twice the frequency of sound wave B. That means that sound wave A must _______________a) travel faster than sound wave Bb) have a shorter wavelength than sound wave Bc) have a lower pitch that sound wave Bd) be louder than sound wave B

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 Example

• http://www.animations.physics.unsw.edu.au/jw/doppler.htm#example

http://www.animations.physics.unsw.edu.au/jw/doppler.htm#example

http://www.animations.physics.unsw.edu.au/jw/doppler.htm#example

Examples/Uses

• Doppler radar: detects storm fronts and their approach speed.

Radar Gun

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 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)

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?


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


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

Section 8: Intensity and Perceived Sound

• The property of sound waves associated with loudness is amplitude

• The property associated with pitch is frequency

• Sound Intensity is the rate of transferring energy through an area

The Decibel Scale

• Threshold of hearing (Io)-

– the minimum intensity sound that can be heard at certain frequencies

Io= 1.0 x 10-12

ß = 0 dB at the threshold of hearing

More on the Decibel Scale

• The decibel scale relates sound intensity to human hearing– An intensity of 0 dB is when there is enough energy

for an average human to detect the sound– 1-dB in intensity level is the smallest change in

loudness that an average listener can detect– If the relative intensity level increases by 10 dB, the

new sound seems approximately twice as loud as the original sound.

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.

waves and sound

Documents

wave particles

water wave

wave travelsex

troughlongitudinal wave

wave pulseunit

spacemechanical wave

wave speed velocity

particles of medium