Sound Waves

What is sound?

• Sound is really tiny fluctuations of air pressure– units of pressure: N/m2 or psi (lbs/square-inch)

• Carried through air at 345 m/s (770 m.p.h) as compressions and rarefactions in air pressure

What IS Sound?

wavelengthcompressed gas

rarefied gas

Sound Waves

• Remember, sound waves are longitudinal waves– Particles of air vibrate in the same direction the

wave travels

Why is Sound Longitudinal?• Waves in air can’t really be transverse, because the

atoms/molecules are not bound to each other– can’t pull a (momentarily) neighboring molecule sideways– only if a “rubber band” connected the molecules would this work– fancy way of saying this: gases can’t support shear loads

• Air molecules can really only bump into one another• Imagine people in a crowded train station with hands in pockets

– pushing into crowd would send a wave of compression into the crowd in the direction of push (longitudinal)

– jerking people back and forth (sideways, over several meters) would not propagate into the crowd

– but if everyone held hands (bonds), this transverse motion would propagate into crowd

Speed of Sound

• 344 m/s in air at 20°C• Depends on:

– Temperature of medium• travels faster at higher temps

– Type of medium• travels better through liquids and solids• can’t travel through a vacuum

Speed of Sound

• Sound speed in air is related to the frantic motions of molecules as they jostle and collide– since air has a lot of empty space, the communication that a

wave is coming through has to be carried by the motion of particles

– for air, this motion is about 500 m/s, but only about 350 m/s directed in any particular direction

• Solids have faster sound speeds because atoms are hooked up by “springs” (bonds)– don’t have to rely on atoms to traverse gap– spring compression can (and does) travel faster than actual atom

motion

Example Sound SpeedsMedium sound speed (m/s)

air (20C) 343

water 1497

gold 3240

brick 3650

wood 3800–4600

glass 5100

steel 5790

aluminum 6420

Speed of Sound in Air

Temperature of Air (ºC) Speed of Sound (m/s)

0 331

25 246

100 386

Human Hearing

sound wave

vibrates ear drum

amplified by bones

converted to nerve impulses in cochlea

Sound hitting your eardrum

• Pressure variations displace membrane (eardrum, microphone) which can be used to measure sound– my speaking voice is moving your eardrum by a mere 1.510-4 mm =

150 nm = 1/4 wavelength of visible light!– threshold of hearing detects 510-8 mm motion, one-half the diameter

of a single atom!!!– pain threshold corresponds to 0.05 mm displacement

• Ear ignores changes slower than 20 Hz– so though pressure changes even as you climb stairs, it is too slow to

perceive as sound• Eardrum can’t be wiggled faster than about 20 kHz

– just like trying to wiggle resonant system too fast produces no significant motion

Human Hearing

• Pitch– highness or

lowness of a sound

– depends on frequency of sound wave

– human range: 20 - 20,000 Hz

ultrasonic waves

subsonic waves

Human Hearing

• Intensity– volume of sound– depends on energy (amplitude) of sound wave– measured in decibels (dB)

Sound frequency• Frequency is equivalent to pitch Humans can hear 20- 20 000 Hz

Demo: How high can you hear?

Elephants & Whales- Infrasonic

Bats & Dolphin- Ultrasonic

http://www.cbmwc.org/education/echo.asp

http://www.seaworld.org/animal-info/info-books/bottlenose/communication.htm

http://www.whaleacoustics.com/audiobaleenwhales.html

Human Hearing

• Humans hear sounds in a limited frequency range20 Hz-20,000 Hz

• Any sound below the human range of hearing is known as an infrasound

• Any sound above the human range of hearing is known as an ultrasound

Human Hearing

7080

100110

120

40

1810

0

DECIBEL SCALE

INTERACTION OF SOUND WAVES

Reflection of sound

When sound encounters an obstacle the sound waves bounce off and reflect

This causes an ECHO

Refraction of Sound

• Sound waves can bend if there are different temperatures in the medium

• The wave always bends towards warmer temperatures

Refraction of sound

Diffraction of Sound• Since sound diffracts, we can hear sound

around corners or through openings• This is why we use megaphones that are

shaped like cones

Doppler Effect

• Doppler Effect– change in wave frequency

caused by a moving wave source

moving toward you - pitch sounds higher

moving away from you - pitch sounds lower

Doppler Effect- Pitch increases as an object approaches and decreases as it moves away.

Click here for simulation

Click here for simulation

Doppler Effect

Stationary (non-moving) source Moving source Supersonic source

same frequency in all directions

waves combine to produce a shock wave called a sonic boom

higher frequency

lower frequency

More about the sonic boom

• Shock wave generated by planes and bullets

Sound Barrier•Mach 1- the speed of sound- 331 m/s or 741 MPH)

•Breaking the Sound Barrier

Chuck Yeager 1947 X-1 SR-71 BlackbirdMach 3.31

F-18 Breaks the Sound Barrier at 741 MPH (approx.)

Click here to see the video!

Seeing with Sound

• Ultrasonic waves - above 20,000 Hz

Medical Imaging SONAR“Sound Navigation Ranging”

Sound

Music Music vs. Noise Resonance Harmonics Interference Acoustics

Music vs. Noise

• Music– specific pitches and sound quality– regular pattern

• Noise– no definite pitch; no set pattern

Resonance

• Forced Vibration– when one vibrating object forces

another object to vibrate at the same frequency

– results in a louder sound because a greater surface area is vibrating

– used in guitars, pianos, etc.

Resonance• Resonance

– A phenomenon that occurs when two objects naturally vibrate at the same frequency

– special case of forced vibration

– object is induced to vibrate at its natural frequency

Resonance

“Galloping Gertie”The Tacoma Narrows Bridge Disaster

Wind through a narrow waterway caused the bridge to vibrate until it reached its natural frequency.

Tacoma Narrow Bridge 1943

VideoTACOMA.mpeg

Harmonics

• Fundamental– the lowest natural frequency of an object

• Overtones– multiples of the fundamental frequency

Constructive - louder

Interference

• Interference– the ability of 2 or more waves to combine to form a

new wave

Destructive - softer

Interference

• Beats– variations in sound

intensity produced by 2 slightly different frequencies

– both constructive and destructive interference occur

Sound Wave Interference and Beats

signal A

signal B

A + B beat(interference)

in phase: add

out of phase: cancel

Beats and Average Frequency

fa - fb = fbeatFrequency A – frequency B = Beat frequency

Ex1: A couple is taking a walk. If Jim takes 264 steps per minute and Sue takes 262 steps per minute, they will be in step twice during a one minute walk and these two steps will be louder than others. The listener will hear a total of 263 steps.

Ex2: If tuning fork A vibrates 264 times each second and fork B vibrates 262 times each second, they will be in step twice each second and the listener will hear a beat of 2 Hz and an overall tone of 263 hertz.

Musicians use beats to tune instruments. Dolphins use to detect motion.

http://library.thinkquest.org/19537/java/Beats.html

Another example of Beats

Beats

AM vs FM Radio

E. Acoustics

• Acoustics– the study of sound

• Reverberation – echo effect produced by

the reflection of sound

Anechoic chamber - designed to eliminate reverberation.

UCSD: Physics 8; 2006

All Shapes of Waveforms• Different Instruments have

different waveforms– a: glockenspiel– b: soft piano– c: loud piano– d: trumpet

• Our ears are sensitive to the detailed shape of waveforms!

• More waveforms:– e: french horn– f: clarinet– g: violin

http://www.st-and.demon.co.uk/AudioMisc/asymmetry/asym.html

How does our ear know?• Our ears pick out frequency

components of a waveform• A DC (constant) signal has no

wiggles, thus is at zero frequency

• A sinusoidal wave has a single frequency associated with it

• The faster the wiggles, the higher the frequency

• The height of the spike indicates how strong (amplitude) that frequency component is

Speakers: Inverse Eardrums

• Speakers vibrate and push on the air– pushing out creates compression– pulling back creates rarefaction

• Speaker must execute complex motion according to desired waveform

• Speaker is driven via “solenoid” idea:– electrical signal (AC) is sent into coil that surrounds a permanent

magnet attached to speaker cone– depending on direction of current, the induced magnetic field

either lines up with magnet or is opposite– results in pushing or pulling (attracting/repelling) magnet in coil,

and thus pushing/pulling on center of cone

Speaker Geometry