Question

The equation of a sound wave in air is P=0.01 cos (1000t – 3x), where P,x,t are in

SI units. The bulk modulus of elasticity is 1.4*105 N/m2. The displacement

amplitude is​

Answer 1

Answer: 24 nm

Explanation:

We are given, Equation of sound wave in air in pressure form i.e.

$P =\Delta P_m cos(\omega t-kx)$

Here, given

$P = 0.01 cos(1000t-3x)$

That is,

$\Delta P_m =0.01 N \\ \\ k = 3m^{-1} \\ \\ \omega =1000 rad/s \\ \\ B= 1.4*10^5 N/m^2$

We know,

Displacement amplitude is given by

$S_o = \frac{\Delta P_m}{B*k}\\ \\= \frac{0.01}{1.4*10^5*3}\\ \\=2.4*10^{-8}m=24 nm$