Pressure Amplitude of 124.5 dB Sound Wave in Air

[Jtappan]

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

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?

 

[anathema]

I would like to offer some corrections and clarifications to your solution.

Firstly, the equation you have used to relate sound intensity (I) and pressure amplitude (P) is incorrect. The correct equation is I = P^2/ρc, where ρ is the density of the medium and c is the speed of sound in that medium. This can be derived from the definition of intensity, which is power per unit area, and the fact that the power of a sound wave is proportional to the square of its amplitude.

Secondly, the reference pressure amplitude for sound in air is not 2*10^-5 N/m^2, as you have used in your calculation. This value is actually the reference sound pressure level (SPL) at a frequency of 1000 Hz, which is used to define the decibel scale. The reference pressure amplitude for sound in air is 20 μPa (microPascals), which is equivalent to 2*10^-5 N/m^2.

Using the correct equation and reference pressure amplitude, we can solve for the pressure amplitude (P) as follows:

124.5 dB = 10 log(I/Io) = 10 log(P^2/ρc / (2*10^-5)^2) = 20 log(P/2*10^-5)
log(P/2*10^-5) = 124.5/20 = 6.225
P = 2*10^-5 * 10^6.225 = 33.576 N/m^2

This matches your result, so the pressure amplitude you calculated is correct.

For the second part of the problem, we can use the formula F = PA, where F is force, P is pressure, and A is area.

F = P * A = 33.576 * 0.520 * 10^-4 = 1.746 mN

Note that the unit for force is mN (millinewtons), not milli N (milliNewtons).

I hope this helps clarify any confusion you had in your solution. As always, it is important to check your equations and units to ensure the correct answer. Keep up the good work as a scientist!

 

[ogb p]

Your approach is mostly correct, but there are a few errors in your calculations. First, the reference pressure amplitude for human hearing is 20 μPa, not 2 N/m^2. So, in your equation for P, it should be P = (20*10^-6)*[10]^6.225 = 33.576 μPa. Then, when calculating the force on the eardrum, you need to convert μPa to N/m^2 by multiplying by 10^-6, giving you a final answer of 1.746 μN.