A sound of wavelength `40 cm` travels in air. If the difference between the maximum and minimum pressures at a given point is `2.0 xx 10^(-3)N//m^(2)`, find the amplitude of vibration of the particles of the medium, The bulk modulus of air is `1.4 xx 10^(5)N//m^(2)`.

Explanation

The pressure amplitude is
`P_0 = (2.0xx 10^(-3)N"/"m^2)/(2)= 10^(-3)N"/"m^2`
The displacement amplitudes `S_0` is given by
`0 = B k"" S_0`
or, `S_0= (P_0)/(Bk)= (P_0 lambda)/(2pi B)`
`=(10^(-3)N"/"m^2 xx (40xx 10^(-2)m))/(2xx pi xx 14 xx 10^(4)N"/"m^2) = (100)/(7pi)A = 6.6A`.