1. Calculating sound properties 2/7/11
Assignment #2
Calculating sound properties
2/7/11

2. Impedance of different media#4
Correction to lecture #2
Impedance of different media
Medium
Speed of sound (cm/s)
Density
(g/cm3)
Impedance
(rayleighs)
(rayls)
Air
3.4 x 104
40.7
Water
1.5 x 105 1
Rock
2 x 105 2
4 x 105
Names for Lord Rayleigh. But Rayleigh is unit of light intensity in photons / cm2 s. This is sound impedence in Rayls.
Table 2.1

3. Stupid Units!! In CGS units In MKS units So CGS rayl = 10 MKS rayl
Let’s agree not to use Rayls at all

4. Units Mass Length Time combo Typical units Velocity L / T m / s
Acceleration
L / T2
m / s2
Force = mass * acceleration
M L / T2
kg m / s2 = N
Pressure = force / area
M / L /T2
kg / m /s2 = N/m2 = Pa
Work, energy=force * distance
M L2 / T2
kg m2 / s2 = Nm = Joule
Intensity=energy / area / time
M / T3
J / m2 / s = kg/m3

5. #1a. Antarctica
Sound velocity at 0 C=273K

6. #1a. Sub Sahara
Sound velocity at 40 C=313K

7. #1b. Time difference Time for warning signal to go 500 m Antarctica
Time = distance / velocity
Antarctica
500 m / (331 m/s) = 1.50 s
Sub Sahara
500 m / (355 m/s) = 1.40 s
Does it matter? It depends on a penguin’s reaction time. Probably 0.1s difference won’t matter.

8. #2. Sound velocity in sea waterB)
Sound moves 56x faster than car and 5.6x faster than plane

9. #2c) Sound velocity in air
Why are you and I glad planes travel slower than this?
We don’t have to listen to sonic booms when the plane creates a loud shock wave.

10. #3. Impedance = density * sound velocity Z =  c
a) Sea water
b) Air

11. #3. Impedances c) Reflectance coefficient
d) Fraction of energy transmitted through

12. Problem #4 - Units Minimum detectable pressure
PR=2x10-5 Pa
Minimum detectable intensity
I = PR2 / Z
Note: Pressure has units of Pascals (Pa)

13. #4a) Minimum detectable intensity for humans

14. #4b. Dolphin minimum detectable pressure
Minimum detectable amplitude -60dB
Reference pressure 0.1 Pa

15. #4c. Dolphin minimum detectable intensity

16. Comparison of sensitivity
Minimum detectable intensity
Human 9.8 x J/m2 s
Dolphin 6.4 x J/m2 s
So which one is more sensitive?
Dolphin is 152 times more sensitive as it takes 152 x lower sound intensity to stimulate the dolphin’s ear
Takes 152 times more energy to stimulate a human ear than a dolphin ear

17. Relative magnitudes Change Intensity Pressure = amplitude 2x 3 dB 6 dB

18. Math refreshers at Mathbench