sound wave

logistic_guy

Senior Member
Joined
Apr 17, 2024
Messages
1,268
(a)\displaystyle \bold{(a)} Calculate the maximum displacement of air molecules when a 210\displaystyle 210-Hz\displaystyle \text{Hz} sound wave passes whose intensity is at the threshold of pain (120 dB)\displaystyle (120 \ \text{dB}). (b)\displaystyle \bold{(b)} What is the pressure amplitude in this wave?
 
(a)\displaystyle \bold{(a)} Calculate the maximum displacement of air molecules when a 210\displaystyle 210-Hz\displaystyle \text{Hz} sound wave passes whose intensity is at the threshold of pain (120 dB)\displaystyle (120 \ \text{dB}). (b)\displaystyle \bold{(b)} What is the pressure amplitude in this wave?
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem
 
(a)\displaystyle \bold{(a)}

Sound intensity formula is:

β=10log10II0\displaystyle \beta = 10\log_{10}\frac{I}{I_0}

We solve for sound intensity I\displaystyle I.

120=10log10I1012\displaystyle 120 = 10\log_{10}\frac{I}{10^{-12}}

This gives:

I=1 W/m2\displaystyle I = 1 \ \text{W}\text{/m}^2

The maximum displacement is given by:

I=2π2ρf2DM2v\displaystyle I = 2\pi^2\rho f^2D^2_Mv

1=2π2(1.29)(210)2DM2(343)\displaystyle 1 = 2\pi^2(1.29)(210)^2D^2_M(343)

This gives:

DM=5.1×105 m\displaystyle D_M = \textcolor{blue}{5.1 \times 10^{-5} \ \text{m}}
 
Top