Sound

• Acoustics is the study of sound.

• All sounds are waves produced by vibrating objects - tuning forks, vocal chords, reeds, lips, columns of air, strings, cricket legs

• Demo – tuning forks - water

Sound

Sound Waves• Sound is a longitudinal wave with

compressions and rarefactions.

Sound Wavespage 272

Sound Waves

• Notice that the air molecules move in a direction parallel to the direction of the wave.

• Demo – Slinky on the floor.

Speed of Sound

• The speed of propagation

Medium Speed of sound

Air 343 m/s

Steel 5100 m/s

Water 1370 m/s

Vacuum 0 m/s

Speed vs Temp

• As temperature increases, the speed of sound increases.

0.6 m/s per oC

Speed of Sound vs Speed of Light

Sound = 343 m/s

Light = 300, 000, 000 m/s

Notice that light travels much faster.

Lightning & Thunder

• Light reaches you in an extremely short period of time.

• Sound reaches you at a much slower rate. It takes about 5 seconds to travel 1 mile.

The delayed sound reachingyour ear after the light.

• Other examples include – starters pistol, chopping wood

• You see the event(light), count the number of seconds until the sound arrives. 5 seconds = 1 mile 10 seconds = 2 miles

Figure 14-36Problem 14-59

Path that sound travels in your earSequence of vibrations from the source•To the ear drum•To the bones in the middle ear•To the oval window in the middle ear•To the fluid in the inner ear•To the hairs in the cochlea in the inner ear•To the nerves which go to the brain on the auditory nerve.

Pitch

• The pitch is determined by the frequency of the sound. Units are Hz or vibrations per sec.

• Humans hear 20 to 20,000 Hz

Loudness of Sound

• How loud a sound seems is determined by the wave’s amplitude. This is proportional to its energy.

• We use a decibel scale to measure loudness.

Sound

• Loud noises can damage your hearing. This usually lowers your upper limit. The tiny hairs in the inner ear may fall out.

Loudness

Sound DecibelsHearing

threshold0

Rustle of leaves 10

Conversation 60

Rock Concert 110

Pain Threshold 120

Jet Engine 130

Reflection of Sound

• Reflection of sound is called an echo.

• Sound waves reflect off of hard smooth surfaces.

• Curtains and rugs results in most of the sound being absorbed

Doppler effect

A change in frequency (pitch) of sound due to the motion of the

source or the receiver

                           

Johaan Christian Doppler1803-1853

Doppler EffectDoppler: Source Doppler: Observer

                                                                                    

Approaching, the frequency is higher because the wavefronts are closer together in time.   Departing, the frequency is lower.

Sound - resonance

• Sound is produced by vibrating systems.• All systems have one or more natural

frequencies.• A natural frequency is the frequency at

which a system tends to vibrate in the absence of any driving or damping force.

Sound - resonance

• If a system is exposed to a vibration that matches its natural frequency, it will vibrate with an increased amplitude.

• This results in the amplification (increase in amplitude). of that frequency

• This phenomenon is called resonance.

Sound - resonance

• When resonance occurs in systems standing waves are formed.

Sound - resonance

•In order for standing waves to form in a closed pipe (closed at one end), the length of the pipe L must be an odd multiple of one fourth of the wavelength.•The necessary condition is that there is a node at the closed end, and an antinode at the open end.

Sound - resonance

1,3,5,7...4

4 1,3,5,7...

nL n

Ln

n

Standing Waves in a Pipe That Is Open at One End(Closed Pipe)

Sound - resonance

for ,

.2

The air column lengths at which resonance

a given frequency occurs

increase in steps of

Sound - resonance

•In order for standing waves to form in an open pipe (open at both ends), the length of the pipe L must be a whole number multiple of one half of the wavelength.•The necessary condition is that there are antinodes at both ends.

Sound - resonance

1, 2,3...2

2 1, 2,3...

nL n

Ln

n

Sound - resonance

for ,

.2

The air column lengths at which resonance

a given frequency occurs

increase in steps of

Figure 14-29Standing Waves in a Pipe That Is Open at Both Ends

Sound - resonance

•Because the speed of sound in air is constant, we can only vary pipe length or frequency to obtain conditions needed for resonance.

Sound - resonance

Example:A tuning fork with a frequency of 392 Hz is found to cause resonance in an air column spaced by 44.3 cm. the air temperature is 27oC. Find the velocity of sound in air at that temperature.

Sound - resonance

.

2 44.3 88.6 .886

392 .886 3

:

4

7.

3

half wavele

Example

We know that resona

ngths

T

nce lengt

herefore cm cm m

mv f

hs are sp

Hz

ace y

m

d

s

b

Terminology – specifically for vibrating air columns.(pipes)

Fundamental frequency – (first harmonic) -the frequency of the longest standing sound wave that can form in a pipe.

Second harmonic – two times the frequency of the longest standing sound wave that can form in a pipe.

Third harmonic – three times the frequency of the longest standing sound wave that can form in a pipe.

Sound - resonance

Beats –Beats occur when two waves of slightly different frequencies are superimposed. A pulsating variation in loudness is heard.

Sound - resonance

Waves on a string – the necessary condition for

standing waves on a string, is that a node exist at either end.

Sound - resonance

1

1

1

2

( ) 2

L

where L the length of the stringvThe fundamental frequency fi

As a consequence the wavelength ofthe fundamental frequency

rst harmonic is fL

where v is the velocity of waves traveling

is

on

the string

Sound - resonance

1 1, 2,3

,..

.

n

n

Subsequent allowable frequencies f

are whole number multiples of the

fundamental frequenc

n

y

f nf

Sound - resonance

1

2= 1,2,3,..

.

n

n

Subsequent allowable wavelengths

e

n

a

L

n

r

n

Figure 14-24aHarmonics

Figure 14-24bHarmonics

Figure 14-24cHarmonics

Sound - resonance

Example: One of the harmonics on a string 1.3 m long has a frequency of 15.6 Hz. The next higher harmonic has a frequency of 23.4Hz. Find (a) the fundamental frequency, and (b) the speed of the waves on this string.

Sound - resonance

1 1 1 1

1 1

1

23.4 15.6 7.80

22

7.8 2 1.30 20.28

n nf f n f nf f

Hz Hz Hz

vf v f L

Lm

Hz ms