Question

the amplitude of the oscillations if the frequency is 500 Hz. Assume an air density of $1.29kg/m^3$ and a velocity of sound is 345 m/s.

Answer 1

Pressure amplitude $P_0$ and amplitude of oscillations $A$ are related by ,

$P_0=\left(\rho v\omega \right)A=(\rho v\times 2\pi f)A$ ,

where $\rho =$ density of medium ,

$v=$ speed of sound in air ,

$f=$ frequency of sound ,

given $\rho =1.29kg/m^3,v=345m/s,f=500Hz$ ,

for $P_0=2\times {10}^{-5}N/m^2$ ,

$2\times {10}^{-5}=1.29\times 345\times 2\times 3.14\times 500\times A$ ,

or $A=\frac{2\times {10}^{-5}}{1.29\times 345\times 2\times 3.14\times 500}=1.43\times {10}^{-11}m$ ,

for $P_0^{\prime }=28N/m^2$ ,

$28=1.29\times 345\times 2\times 3.14\times 500\times A^{\prime }$ ,

or $A^{\prime }=\frac{28}{1.29\times 345\times 2\times 3.14\times 500}=2.01\times {10}^{-5}m$