Announcements

- Homework 21: due Today

- Homework 22: due Thursday, Dec. 2

- Review session: Sunday, Dec. 5, 1-4 pm?

• Sound waves are the most important example of longitudinal waves.

• They can travel through any material, except vacuum (no one can hear you scream in outer space).

• Speed of sound depends on material (and temperature)

Chapter 17: Waves-II (Sound waves)

Reading assignment: Chapter 18.1-18.4

Homework : (due Monday, Nov. 14, 2005):

Sound Waves

Sound waves are longitudinal waves.

They consist of compressed and rarified regions of gas (medium)

We can hear (audible) frequencies from about 20 Hz (low) to 15,000 Hz (high).

Infrasonic “sound” waves: below ~ 20 Hz

Ultrasonic sound waves: above ~ 15,000 Hz

Sound

- is a wave (sound wave)

- Rarefied and compressed regions

- Longitudinal wave

- air molecules move back and forth

Sound waves, hearing and the ear

http://www.innerbody.com/anim/ear.html

Notes and their fundamental frequency

Octaves: Frequency doubles for each tone

Speed of Sound Waves

B

v

Y… Young’s modulus (see Chapter 13.6)

B… Bulk modulus of medium (see Chapter 13.6)

…density of material

Bulk modules determines the volume change of an object due to an applied pressure P.

ii VV

P

VV

AFB

//

/

strain volume

stress volume

Y

v

In gas and liquids: In solids:

iLL

AFY

/

/

strain tensile

stress tensile

Young’s modules determines the length change of an object due to an applied force F.

Speed of Sound in air as a function of temperature

m/s 343 v:20 @273

1)m/s 331( :airin sound of Speed

S

CC

Tv C

TC … air temperature in degrees Celsius

Black board example 18.1

(a) How long does it take the light (c = 300,000,000 m/s) to get to you?

(b) How long does it take the sound of thunder to get to you (Temp= 20ºC = 68F ).

(c) How far does the sound travel in one second?

Lightning strikes 10 miles (16090 m) away from you.

Periodic sound waves.

Condensation:

Regions of compressed gas.

Rarefactions:

Regions of rarefied gas.

Distance between two compressed regions: Wavelength

(A constant tone is a periodic sound wave)

Periodic sound waves.

tkxs costx,s max

tkxP sintx,P max

Displacement of small volume element:

Pressure variation:

Standing waves in air colums

• Standing waves can be set up in a tube or air (pipe, flute, …)

• Distinguish between open end pipes and close end pipes

• Analogous to standing waves on a string.

• Antinode on open ends. Node on closed ends.

Both ends open:

Standing waves in air colums

• Antinode on open ends.

• Node on closed ends.

One end closed:

In a pipe open at both ends, the natural frequencies of oscillation form a harmonic series that includes all integral multiples of the fundamental frequency

... 3, 2, 1,n 2

L

vn

vf

nn

In a pipe closed at one end and open at the other, the natural frequencies of oscillation form a harmonic series that includes only odd integer multiples of the fundamental frequency.

... 5, 3, 1,n 4

L

vn

vf

nn

A loudspeaker is adjustable in frequency from 1000 to 2000 Hz. The tube D is a piece of cylindrical sheet-metal pipe 45. 7 cm long and open at both ends.

(a) If the speed of sound in air is 344 m/s, what is

the lowest frequency at which resonance will occur in the pipe when the frequency emitted by the speaker is varied from 1000 Hz to 2000 Hz?

(b) Sketch the standing wave for each resonant frequency.

Black board example 18.2

HW 18.35

Combining different harmonics

Music instruments

Doppler effect

When heading into waves: Frequency becomes shorter.

When heading away from waves: Frequency becomes larger.

Doppler effect

When heading into waves: Frequency becomes shorter.

When heading away from waves: Frequency becomes larger.

Doppler effect

Moving detector Moving source

fv

vvf D

' fvv

vf

S

'

+… detector moving toward source

- … detector moving away from source

+… source moving away from observer

- … source moving towards observer

fvv

vvf

S

D

'If both, detector and source are moving:

Black board example 18.3

Homework 18.47

The 16,000 Hz whine of the turbines in the jet engines of an aircraft moving with speed 200 m/s is heard at what frequency by the pilot of a second craft trying to overtake the first at a speed of 250 m/s?

Shock waves

When the speed of the object, vS, exceeds the wave speed, v.

The ratio vS/v is called the Mach number.

For sound: Mach 3 means 3x the speed of sound.

ss v

v

tv

tv

sin