Sound Waves

• Mechanical Waves (require a medium)

• Longitudinal waves

• Formed by a series of compressions and rarefactions.

Frequencies of Sounds

Infrasonic Sound

(elephants can hear)

f < 20 Hz

Audible Sounds

(humans can hear)

20 – 20,000 Hz

Ultrasonic Sound

(dolphins can detect)

f > 20,000 Hz

Incr

easi

ng F

requ

ency

Pitch• How high or low we perceive a sound to

be, depending on the frequency of the sound wave.

• As the frequency of a sound increases, the pitch of that sound increases.

A

B

C

Which graph represent the sound with the highest pitch?

CWhat is wrong with these graphs representing sound waves?

Sound is longitudinal, not transverse.

Ultrasound• Images produced by ultrasonic sound

show more detail then those produced by lower frequencies.

• Ultrasonic sound has many applications in the field of medicine.

• Ultrasound images, such as the one shown here, are formed with reflected sound waves.

Amplitude

• The amplitude of a sound wave corresponds with how loud the sound is.– A large amplitude is a loud sound.– A small amplitude is a quiet sound.

Practice• Draw a loud and high pitched wave.

• Draw a loud and low pitched wave.

• Draw a quiet sound wave with medium pitch

Speed of sound depends on medium and temperature.Medium V (m/s)

Gas: air (0oC) 331

Gas: air (25oC) 346

Gas: air (100oC) 366

Liquid: water (25oC) 1490

Solid: copper (density = 8.96g/cm3) 3560

Solid: aluminum (density = 2.70g/cm3)

5100

Source: Serway/Faughn, p. 461 (Table 14.1)

To calculate the speed of sound through air at different temperatures…

vsound

(331m / s)T

273K

331 m/s is the speed of sound at 0oC

T = temperature in Kelvin

Remember: Kelvin = oC + 273

Sound waves propagate in 3D

• Sound waves travel away from a vibrating source in all directions.

• In these spherical waves, the circles represent compressions (wave fronts).

Source

Wave front

Intensity• Intensity (I) of a wave is the rate at which

energy flows through a unit area (A) perpendicular to the direction of travel of the wave.

• However, power is also the rate at which energy is transferred (W = J/sec)

• And sound waves are spherical, so the power is distributed over the surface area of a sphere (4r)

24 R

P

area

powerI

I = Intensity (W/m2)

P = Power (W)

R = Distance from source (m)

What is the intensity of the sound waves produced by a trumpet at a distance of 3.2 m when the

power output of the trumpet is 0.20 W?

24 R

PI

2)2.3(4

20.0

m

WI

23106.1m

WI

Human Hearing - Frequency• The range of human hearing is generally

considered to be from about 10 Hz to about 20,000 Hz.

• In reality, it’s much worse.

Few people can hear above

14-15 thousand Hz, and it gets

worse as you grow older.

Human Hearing - Intensity• Hearing also depends on the intensity of the

sound. • The softest sound that can be heard by the

human ear has an intensity of 1x10-12 W/m2. This intensity is said to be the Threshold of Hearing.

• The loudest sound the human ear can tolerate has an intensity of 1.0 W/m2. This is known as the Threshold of Pain.

Human Hearing - Decibles

• When dealing with human hearing, the intensity range is very large (1x10-12W/m2 to 1 W/m2).

• A sound with twice the intensity, isn’t heard as twice as loud.

• The ear works on a logarithmic scale. • Sound loudness is measured in decibels (dB)

which compare the sound’s intensity to the intensity at the threshold of hearing.

Conversion of intensity to decibel level

Intensity Decibel (dB) Example

1x10-12 0 Threshold of hearing

1x10-9 30 Whisper

1x10-7 50 Normal Conversation

1x10-4 80 Traffic

1x10-2 100 Fire Engine

1x10 120 Rock Concert

1x102 140 Jet

Decibels and Intensity

• When the intensity is doubled (one person talking vs two people talking) there is a three decibel increase.

• When the intensity is ten times as large there is a ten decibel increase and the noise sounds twice as loud.

Example: A rather noisy typewriter produces a sound intensity of 1 x 10-5 watts/m2 which is 70 dB. Find the decibel level when a second identical machine is added to the office.

Two machines would be 73 dB

Calculating Decibel Level:

= 10 log (I/Io) = 10 log (I/1x10-12)

Where: Io is the threshold of hearing (1x10-12 W/m2)

and is the decibel level

Thus…

Threshold of hearing 0dB

Threshold of pain 120 dB

Doubling the sound intensity is a 3 dB increase.

80 dB

100 dB

120 dB

140 dB

Example: Michael wants to install a 100. W stereo amp in his sweet new VW. What will the dB level be, at his ears, approximately 1.50 m away from the speakers?  

24 R

PowerI

2)5.1(4

100

m

W

2/5.3 mw

212

2

/101

/5.3log10

mW

mW = 125 dB

Note this is three and a half times the threshold of pain.

The Doppler Effect

• Relative motion between the source of waves and the observer creates a change in frequency.

See: http://www.lon-capa.org/~mmp/applist/doppler/d.htm

Non-Java applet:

http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/doppler.htm

Doppler Effect Equation:

s

dsd vv

vvff

fd Perceived frequency heard by the detector

fs Frequency being created by the source.

* Define the + direction to be from the source to the detector

vd velocity of the detector

vs velocity of the source.

V velocity of sound

Doppler effect possibilities:

+

+ Vs - Vd

+

+ Vd - Vs

+

+ Vs + Vd

+

- Vd - Vs

Highest frequency

Lowest frequency

Imagine sitting inside a car. The car’s horn has a frequency of 500

Hz. What frequency would you hear inside the car, moving at 25 mi/hr?

500 Hz

Imagine yourself outside the car

•As the car approaches you, is the frequency higher or lower then 500 Hz?

•As the car passes and leaves you behind, is the frequency higher or lower then 500 Hz?

HEAR DOPPLER CAR

Example: An ambulance moving at 25 m/s drives towards a physics student sitting on the side of the road. The EMTs in the ambulance hear the siren

sounding at 650 Hz. What is the frequency heard by the student? (assume speed of sound is 343 m/s)

+

fs = 650 Hz fd = ?

Vs = + 25m/s Vd = 0 m/s

s

dsd vv

vvff

25343

0343650Hzfd

318

343650Hzfd

HzHzfd2100.7701

Example: At rest a car’s horn sounds the note A (440 Hz). While the car is moving down the street, the horn is sounded. A bicyclist moving in the same direction with 1/3 the car’s speed hears a lower pitched sound.(A) Is the cyclist ahead of or behind the car?

The observed frequency is lower than the actual frequency, therefore they must be moving apart from one another. This means the cyclist is behind the car because he is moving slower than the car.

Wow, the bike rider is

invisible!

(B) If the car is moving at 33 m/s (with a horn frequency of 440 Hz) and the bike is following the car at 11 m/s, what is the frequency detected by the bicyclist? (assume speed of sound is 343 m/s)

s

dsd vv

vvff

+

fd = ? fs = 440 Hz

Vd = - 11m/s Vs = - 33 m/s

33343

11343440Hzfd

376

354440Hzfd Hzfd 414

Supersonic Movement

Beats

Guitars can be tuned using beats -- tune to “zero beat frequency”

Beats

fb f

1 f

2

• The frequency of the resulting beats can be calculated by:

A certain piano key is suppose of vibrate at 440 Hz. To tune it, a musician rings a 440 Hz tuning fork at

the same time as he plays the piano note and hears 4 beats per second. What frequency is the piano emitting if the note the piano plays is too high?

fb f

1 f

2

4 Hz = 440 - f2

f2 = 436 Hz

4 Hz = f1 - 440

f1 = 444 Hz

Beats can also occur from two sources playing the same frequency

Along the yellow lines there is destructive interference. There is no wave disturbance there.

Constructive Interference

Destructive Interference

Constructive Interference (n=0)

Constructive Interference (n=1)

Destructive Interference (n=0)

Destructive Interference (n=1)

Standing Waves• Wave pattern that results when two

waves of the same f, , and A travel in opposite directions and interfere.

• The resultant of the two waves appears to be standing still.

Resonance• The tendency of a system to vibrate with

maximum amplitude at a certain frequency.

• When a system is in resonance, a small input of energy leads to a large increase in amplitude.– Examples: being pushed on a swing.– Tacoma Narrows Bridge

Example: Blowing over a bottle of water will produce resonance.

• The water stops the sound so it is a node.

• The air is free to move at the top of the bottle, so it is an antinode.

• Going from node to the first antinode, is ¼ of a wave.

• Therefore, the length of the bottle is ¼th the wavelength.

L

L

44

1

Example: Blowing over a bottle of water will produce resonance. If the column of air in the

bottle is 16.0 cm long, what is the resonant frequency of the bottle? (assume vsound = 343 m/s)

m

m

L

L

64.0

)160.0(4

44

1

fv

)64.0(343 f

Hzf 536

Resonance in a TubeTuning fork with frequency of 958 Hz

Length of tube out of the water = ?

Assume the speed of sound is 345 m/s.There is a quarter of a wave in the tube.

L 14 = 4L

f v

v4L

L = 9.00 cm

Harmonics• Sometimes more than one size wave will fit the given

parameters (node or antinode at the end). These different wave sizes are called harmonics.

•First harmonic (or fundamental frequency) is the largest wave that fits the parameters.

•Second harmonic (first overtone) is the second largest wave that fits the parameters.

Tube with two sides openExample: Flute

Fundamental frequency (first harmonic)

L = ½

Second Harmonic(First Overtone)

L =

Third Harmonic(Second Overtone)

L = 3/2 or 1 ½

Tube with one side open & one side closedExample: - Blowing over the top of a bottle

- PanpipesFundamental frequency (first harmonic)

L = ¼

Second Harmonic(First Overtone)

L = ¾

Third Harmonic(Second Overtone)

L = 5/4 or 1 ¼

Tube with both sides closed or String held on both ends.

Example: Guitar, harp, piano, violin

Fundamental frequency (first harmonic)

L = ½

Second Harmonic(First Overtone)

L =

Third Harmonic(Second Overtone)

L = 3/2 or 1 ½

• Good applet on harmonics:• http://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.html