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) = (2.0 xx 10^(-3) N//m^(2))/(2) = 10^(-3) N//m^(2)`.
The displacement amplitude `s_(0)` is given by
`p_(0) = B k s_(0)`
or, `s_(0) = (p_(0))/(Bk) = (p_(0)k)/(2piB)`
`= (10^(-3)N//m^(2) xx (40 xx 10^(-2)m))/(2 xx pi xx 14 xx 10^(4)N//m^(2)) = (100)/(7pi)Å`
`= 4.54 Å`