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Find the following for given wave equati...

Find the following for given wave equation.
`P = 0.02 sin [(3000 t =- 9 x]` (alll quantities are in `S.I.` units.)
(a) Frequency , (b) Wavelength , (c) Speed of sound wave
(d) If the equilibrium pressure of air is in `10^(5)` Pa then find maximum and minimum pressure.

Text Solution

Verified by Experts

(a) Comparing with the standard from of a travelling wave
`p = p_(0) sin[omega (t - x//v)]`
we see that `omega = 3000 s^(-1)`. Then frequency is
`f = (omega)/(2pi) = (3000)/(2pi) Hz`
Also from the same comparison, `omega//v = 9.0 m^(-1)`.
or, `v = (omega)/(9.0m^(-1)) = (3000s^(-1))/(9.0m^(-1)) , (1000)/(3)m//s`
The wavelength is `lambda = (v)/(t) = (1000//3m//s)/(3000//2piHz) = (2pi)/(9)m`
(b) The pressure amplitude is `p_(0) = 0.02 n//m^(2)`. Hence, the maximum and minimum pressure at a point in the wave motion will be `(1.0 xx 10^(5) +- 0.02) N//m^(2)`.
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