Plane harmonic waves of frequency 500 Hz are produced in air with displacement amplitude of `10mum`. Given that density of air is `1.29(kg)/(m^3)` and speed of sound in air is `340(m)/(s)`. Then

Options

A. The pressure amplitude is `13.76 Nm^(-2)`
B. The energy density is `6.45 xx 10^(-4)Jm^(-3)`
C. The energy flux is `0.22 Jm^(-2)s^(-1)`
D. Only (A) and (C) are correct

Answer

A, B, C

Explanation

Given that
n = 500Hz
`A = 10 xx 10^(-6)m`
`rho = 1.29kg//m^(3)`
v = 340m/s
`v = sqrt((B)/(rho))`
`B = rhov^(2) = 1.29 xx (340)^(2) = 1.49 xx 10^(5)N//m^(2)`
`lambda = (v)/(lambda) = (340)/(500)` = 0.68m
Pressure amplitude
`DeltaP = (2pi)/(lambda) AB`
= `(2pi)/(0.68) xx 10 xx 10^(-6) xx 1.49 xx 10^(5)` = 13.76 m
Energy density `(P)/(Sv) = 2pi^(2)n^(2)A^(2)rho`
= `2 xx 10 (500)^(2) xx (10 xx 10^(-6))^(2) xx 1.29`
= `6.45 xx 10^(-4)J//m^(3)`
`mu_(phi) = (P)/(S) = 2pi^(2)n^(2)A^(2)rhov` = `0.22 J//m^(2)-s`