1. Purdue University, Physics 220
Lecture 21
Sound
Lecture 21
Purdue University, Physics 220

2. Purdue University, Physics 220
Sound Waves
Lecture 21
Purdue University, Physics 220

3. Purdue University, Physics 220
Speed of Sound
In gas: the speed of sound depends on the composition and is proportional to the square root of the absolute temperature,
Medium
Speed (m/s)
Air
343
Helium
1000
Water
1480
Steel
5790
Comparison of speed in solid, liquid, gas, helium is fun here.
T in Kelvin
T = 0 0C or 273 K
Lecture 21
Purdue University, Physics 220

4. Purdue University, Physics 220
Law of Refraction 1 2
When wave enter the material in which its speed is different
f – frequency does not change
But v and  will change according to =v/f
Refraction is the change in the direction of a wave due to a change in its speed
Lecture 20
Purdue University, Physics 220

5. Purdue University, Physics 220
Intensity and Pitch
For Sound Waves
I = p02 / (2 r v) (po is the pressure amplitude)
Proportional to p02
Loudness
Loudness perception is logarithmic
Threshold for hearing I0 = W/m2
b = (10 dB) log10 ( I / I0)
b2 – b1 = (10 dB) log10(I2/I1)
Pitch
Perception of frequency
Lecture 21
Purdue University, Physics 220

6. Purdue University, Physics 220
Decibels
Sound intensity level 
 = (10 dB) log10 ( I / I0)
Units: Bels
A ratio of 107 indicates a sound intensity of 7 bels or 70 decibels (dB)
An intensity of 0 dB corresponds to the hearing threshold
Intensity increase by factor 10  intensity level adds 10 dB
Adding 3 dB to the intensity level doubles the intensity (log102=0.3)
Alexander Graham Bell
( )
Lecture 21
Purdue University, Physics 220

7. Purdue University, Physics 220
Question
If 1 person can shout with loudness 50 dB. How loud will it be when 100 people shout?
A) 52 dB B) 70 dB C) 150 dB
b100 – b1 = (10 dB) log10(I100/I1)
b100 = 50 + (10 dB) log10(100/1)
b100 =
Lecture 21
Purdue University, Physics 220

8. Purdue University, Physics 220
Standing Sound Waves
Pipe open at both ends
Lecture 21
Purdue University, Physics 220

9. Purdue University, Physics 220
Standing Sound Waves
Pipe open at one end
Lecture 21
Purdue University, Physics 220

10. Standing Waves in Pipes
Open at both ends:
Pressure node at end
l = 2 L / n n=1,2,3, ...
Open at one end:
Pressure antinode at closed end: l = 4 L / n
n=1,3,5, ...
Lecture 21
Purdue University, Physics 220

11. Purdue University, Physics 220
Organ Pipe Example
A 0.9 m organ pipe (open at both ends) is measured to have it’s n=2 harmonic at a frequency of 382 Hz. What is the speed of sound in the pipe?
Pressure node at each end.
l = 2 L / n n=1,2,3..
l = L for n=2 harmonic
f = v / l
v = f l
= (382 s-1 ) (0.9 m)
= 343 m/s
Lecture 21
Purdue University, Physics 220

12. Purdue University, Physics 220
iClicker
What happens to the fundamental frequency of a closed pipe, if the air (v=343 m/s) is replaced by helium (v=972 m/s)?
A) Increases B) Same C) Decreases
Lecture 21
Purdue University, Physics 220

13. Purdue University, Physics 220
Timbre
Fourier decomposition
Fundamental + Overtones
Lecture 21
Purdue University, Physics 220

14. Superposition & Interference
Consider two harmonic waves A and B meeting at x=0.
Same amplitudes, but 2 = 1.15 x 1.
The displacement versus time for each is shown below:
A(1t)
B(2t)
What does C(t) = A(t) + B(t) look like?
Lecture 21
Purdue University, Physics 220

15. Superposition & Interference
Consider two harmonic waves A and B meeting at x=0.
Same amplitudes, but 2 = 1.15 x 1.
The displacement versus time for each is shown below:
A(1t)
B(2t)
CONSTRUCTIVE INTERFERENCE
DESTRUCTIVE INTERFERENCE
C(t) = A(t) + B(t)
Lecture 21
Purdue University, Physics 220

16. Purdue University, Physics 220
Beats
Add two cosines and remember the identity:
where
and
cos(Lt)
Beat Frequency:
Lecture 21
Purdue University, Physics 220

17. Doppler Effect Moving Source
Lecture 21
Purdue University, Physics 220

18. Doppler Effect Moving Source
When source is coming toward you (vs > 0)
Distance between waves decreases
Frequency increases
When source is going away from you (vs < 0)
Distance between waves increases
Frequency decreases
fo = fs / (1- vs/v)
Lecture 21
Purdue University, Physics 220

19. Purdue University, Physics 220
iClicker
A police car passes you with its siren on. The frequency of the sound you hear from its siren after the car passes
A) Increases B) Decreases C) Same
Lecture 21
Purdue University, Physics 220

20. Doppler Effect Moving Observer
Lecture 21
Purdue University, Physics 220

21. Doppler Effect Moving Observer
When moving toward source (vo < 0)
Distance between waves decreases
Frequency increases
When away from source (vo > 0)
Distance between waves increases
Frequency decreases
fo = fs (1- vo/v)
Lecture 21
Purdue University, Physics 220

22. Moving Observer and Source
Combine: fo = fs (1-vo/v) / (1-vs/v)
A: You are driving along the highway at 65 mph, and behind you a police car, also traveling at 65 mph, has its siren turned on.
B: You and the police car have both pulled over to the side of the road, but the siren is still turned on.
In which case does the frequency of the siren seem higher to you?
A) Case A B) Case B C) same vs f vo f’ v
Lecture 21
Purdue University, Physics 220