IB Physics

Waves and Sound

The 5 Properties of Waves Rectilinear Propagation: waves

propagate (move or spread out) in straight lines in all directions away from the source.

Reflection: change in direction of a wave at an interface between two different media so that the wave returns into the medium from which it originated.

Refraction: change in direction of a wave due to a change in its speed. This is observed when a wave passes from one medium to another.

Diffraction: bending of waves around small obstacles and the spreading out of waves passing through small openings.

Interference: the addition (superposition) of two or more waves that results in a new wave pattern.

The 5 Properties of Waves

Any Wave: is a traveling disturbance that carries energy.

Web Link: The Wave

Two types of waves:1) Transverse – the disturbance is perpendicular to

the direction the wave is traveling

2) Longitudinal – the disturbance is parallel to the direction the wave is traveling

Web Links: Longitudinal & Transverse, Longitudinal

?

Consider a transverse wave on a string, frozen in time:

A

A

A = Amplitude

x

y

= wavelength

Now consider the position of one point on the string:

time

y

A

A

T = period

f = frequency = 1/T

Frequency (f), period (T), wavelength (), and wave speed (v) are all related:

If the wave crests are 12 m apart, and you see one pass by you every 3 seconds, how fast are they going?

v = /T v = f

Ex: Radio Waves

Radio waves travel at the speed of light in a vacuum, 3.00 x 108 m/s . Find the wavelength of radio waves from “Light Rock” 106.7 FM.

How long do you think the wavelengths of radio waves are ?

Radio waves are a type of Electromagnetic Waves

Electromagnetic WavesThese don’t need a medium (substance to travel in).

The speed of a wave depends on the medium.

v = f That means that these two are inversely proportional

f

f

All other waves require a medium (air, water, string, etc.)

Waves on a String

We can develop a formula for the speed of waves on a string:

v

What qualities of the string do you think determine this speed??

Ex:

The rope has a length of 1.2 m and a mass of 2.0 kg. If he shakes the end 4.0 times a

second, and it yields the pattern shown, what is the tension in the rope?

Sound Waves *any longitudinal waves

Sound waves in air consist of vibrating

air moleculesWeb Link: Loudspeaker

Compare a longitudinal wave in a slinky to a sound wave in a tube:

A = pressure amplitude = max. change in pressure

very small for common sounds ( 3x10-2 Pa)

Loudness is related to pressure amplitude

Frequency of Sound Waves: number of cycles per second

Healthy young ears can hear frequencies between:

20 Hz 20,000 Hz

Which end do we lose with age?

UltrasonicInfrasonic

Pure tone – a single frequency sound

(most sounds are composed of many frequencies)

Ex: Lightning & Thunder

Speed of Sound depends on the medium

(gas, liquid or solid)

vsound in air = 343 m/s (767 mi/hr)

How can you tell how far away the storm is ??

Speed of sound in an ideal gas

vkTm

k = 1.38 x 10-23 J/K (Boltzmann const.)

T = Kelvin temperature

m = molecular mass

= CP/CV

Ex:

Verify the speed of sound in air if the average air molecule mass is

28.9 u, and = 1.40 for air.

Speed of sound in a liquid

vB ad

Bulk Modulus (adiabatic)

Density of liquid

Ex: Water

The speed of sound in water is around 1500 m/s

(that’s over 4 times as fast as it travels in air!)

Speed of sound in solid bars

vY

Young’s Modulus

Ex: Train Tracks

Sound Intensity

of the sound wave

to the wave

IPA

SI unit =

Sound Intensity = Pow erArea

Spherically Uniform Sound:

Area = 4r2IPA

P4 r 2

How much less is the sound intensity for the person that is farther away?

600 m

200 m

Ex: Fireworks

To compare two intensities (I and I0):

(in decibels) = 10 log (I/I0)

Notes on Sound Intensity

Intensity is related to loudness (but not directly proportional)

10-12 W/m2 = lower threshold of human hearing

1 W/m2 = enough to cause ear damage

Different sound intensities are compared using:

decibels (dB)

“Intensity Level” (unitless)

For sound meters, I0= threshold = 10-12 W/m2

Ex:

If a sound meter picks up an intensity of 2 x 10-11 W/m2 , what

will be the intensity level reading?

Ex:

If you bring a decibel meter to a rock concert, at what decibel reading should you start

worrying about ear damage?

(James Taylor would never play this loud……)

Ex:

Standing 3 times as far from a uniform sound source will decrease the intensity

level by how many decibels?

Some interesting applications of Sound Waves

Sonar:

Ex: Dolphins

Ex: Web Link: Ocean floor mapping

Ultrasound:

Web Link: How does Ultrasound work?

Cancer treatment:

Web Link: Local Hyperthermia

The Doppler Effect-the change in wave frequency resulting from motion of the source or observer

Consider the waves from a sound source:

Now, consider the waves from a moving source:

You hear a lower frequency as it moves away

from you

You hear a higher frequency as it moves toward

you

Web Links: Doppler Effect I and II

Doppler Effect (1 source)

Here’s how to calculate the frequency heard by the observer:

f’ = perceived frequency

f = actual frequency

vs = speed of the source

v = speed of the wave

f f1

1v

vs

f f1

1v

vs

Source moves toward still observer

Source moves away from still observer

Ex:

If the fire engine has a speed of 30 m/s, and its siren has a frequency of 500 Hz, what frequency does the pedestrian hear as it moves

a) toward him ?

b) away from him ?

Now, if the observer is moving at speed vO…..

f f 1

vv

o

toward the source:

f f 1

vv

o

away from the source:

Web Link: Doppler effect in acoustics

Now, if both observer and source are moving…

vs

vo

(signs determined as before)

vv

1

vv

1f f

s

0