Answer Pressure & Force on Ear Drum: 33.576 N/m2 & 1.746 mN

[Jtappan]

1. Homework Statement

(a) What is the pressure amplitude of a sound wave with an intensity level of 124.5 dB in air?

_____ N/m2
(b) What force does this exert on an eardrum of area 0.520 10-4 m2?

_____ mN



3. The Attempt at a Solution


if P is amplitude of pressure, then sound intensity (I) is proportional to P^2
I/Io = (P/Po)^2
dB = sound intensity level = 10 log[I/Io]
124.5 = 10 log[I/Io] = 10 log[P/Po]^2 = 20 log(P/Po)
log(P/Po) = 124.5/20 = 6.225
P = Po [10]^6.225
Po = reference pressure amplitude for human ear = 2*10^-5 N/m^2
P = 2*10^-5*[10]^6.225
P = 33.576 N/m^2
----------------
Force on eardrum = P * area = 33.576*0.52*10^4 N
F = 1.746 milli N




This is what I did. But it is not giving me the correct answer...can anyone help me?

 

[dlgoff]

The given eardrum area is 0.520*10^-4? But in your force equation (Force on eardrum = P * area = 33.576*0.52*10^4 N) you have it as 0.52*10^4.

 

[ogb p]

Your calculations are correct, but it's possible that the given values for intensity level and eardrum area are rounded or not exact. Therefore, the final answers may not match exactly with the given values of 124.5 dB and 0.520x10^-4 m^2. Additionally, the values for intensity level and eardrum area may have been calculated using different reference values, which could also lead to a slight discrepancy in the final answers. Overall, your approach and calculations seem correct and it's possible that the difference in the final answers is due to rounding or slight variations in the given values.