chapter 16 - sound waves
DESCRIPTION
Speed of Sound Sound Characteristics Intensity Instruments: Strings and Pipes 2 Dimensional Interference Beats Doppler Effect Sonic Boom and shock waves. Chapter 16 - Sound Waves. Sound Speed. Variation with Temperature:. Air. Seawater. Pitch is frequency. - PowerPoint PPT PresentationTRANSCRIPT
Chapter 16 - Sound Waves
• Speed of Sound• Sound Characteristics • Intensity• Instruments: Strings and Pipes • 2 Dimensional Interference• Beats• Doppler Effect• Sonic Boom and shock waves
Sound Speed Bulk modulus Bv
density
Air Sea WaterBulk Modulus 1.4(1.01 x 105) Pa 2.28 x 109 Pa
Density 1.21 kg/m3 1026 kg/m3
Speed 343 m/s 1500 m/s
Variation with Temperature:
mv 331 0.60T
s
2 3 mv 1449.05 4.57T .0521T .00023T
s
Air
Seawater
Pitch is frequency
Audible 20 Hz – 20000 Hz
Infrasonic < 20 Hz
Ultrasonic >20000 Hz
Middle C on the piano has a frequency of 262 Hz.What is the wavelength (in air)?
1.3 m
Intensity of sound• Loudness – intensity of the wave. Energy
transported by a wave per unit time across a unit area perpendicular to the energy flow.
Source Intensity (W/m2) Sound Level
Jet Plane 100 140
Pain Threshold 1 120
Siren 1x10-2 100
Busy Traffic 1x10-5 70
Conversation 3x10-6 65
Whisper 1x10-10 20
Rustle of leaves 1x10-11 10
Hearing Threshold 1x10-12 1
Sound Level - Decibel
0
IdB 10log
I
12
0 2
WI 1x10
m
Stringed instruments
nn
v nvf n=1,2,3,4,....
2L
Question 1
• A steel wire in a piano has a length of 0.9 m and a mass of 5.4 g. To what tension must this wire be stretched so that its fundamental vibration corresponds to middle C: i.e., the vibration possess a frequency 261.6.
Wind instruments – Double open ended pipes
nn
v nvf n=1,2,3,4,....
2L
Frequencies are identical to waves on a string
Wind instruments – Single open ended pipes
nn
v nvf n=1,3,5,7,....
4L
Only odd harmonics are present
Question 2 – Pepsi Bottle
• What is the fundamental frequency of a pepsi bottle 32 cm tall when you blow over it. Assume the speed of sound in air is 343 m/s.
• 5 cm of water are added to the bottle. What is the new resonant frequency.
32 cm
Waves on the surface of a liquid
Two dimensional wave reflection
i r
Interference in Space
When the path lengths from source to receiver differ by /2 destructive interference results.
Interference in Time - Beats
• Two sounds of different frequency:
1 m 1 1 m 1D x 0 D sin k 0 t D sin 2 f t
2 m 2D x 0 D sin 2 f t
• Superposition:
1 2 m 1 m 2D D D D sin 2 f t D sin 2 f t
• Trig identity again:
Interference in Time - Beats
1 2 m 1 m 2D D D D sin 2 f t D sin 2 f t
1 2 1 21 2sin sin 2sin cos
2 2
1 2 1 2m
f f f fD 2D cos 2 t sin 2 t
2 2
Amplitude varies in time at a frequency equal to the difference in the two frequencies
Beat Frequency beat 1 2f f f
Beats
beat 1 2f f f
Doppler Effect
Doppler Effect – 4 cases
• Source moving toward receiver• Source moving away from receiver• Receiver (observer) moving towards source• Receiver (observer) moving away from source.
Source moving case
sv T
vT
s
s
vv 1
v v
ss
v v 1f f
vv 11vv
Towards:s
1f f
v1
v
Away:
Receiver (observer) moving case
O Ov v vf f 1
v
Towards:
O Ov v vf f 1
v
Away:
Source and receiver moving
O
O
s S
v1 v vvf f f
v v v1v
• Numerator – Receiver (observer)– Toward +– Away –
• Denominator – Source– Toward –– Away +
Doppler Example• Intelligence tells you that a particular piece of
machinery in the engine room of a Soviet Victor III submarine emits a frequency of 320 Hz. Your sonar operator hears the machinery but reports the frequency is 325 Hz. Assume you have slowed to a negligible speed in order to better hear the Russian.– Is the VIII coming toward you or moving away from you?
– Assuming the Victor is either moving directly toward or away from you, what is his speed in m/s?
Shock waves and the sonic boom
sound sound
object object
v t v 1sin
v t v m
Sometimes you hear 2 booms