The equation of a sound wave in air is given by `trianglep=(0.02)sin[(3000)t-(9.0)x]`, where all variables are is SI units. (a) find the frequency, wavelength and the speed of sound wave in air. (b) If the equilibrium pressure of air is `1.01xx10^5(N)/(m^2)`, What are the maximum and minimum pressure at a point as the wave passes through that point?

Explanation

a. comparing with the standard form of a travelling wave,
`trianglep=trianglep_(max)sin[omegat-(x)/(v)]`
we see that `omega=3000s^-1.` The frequency is
`f=(omega)/(2pi)=(3000)/(2pi)Hz`
Also from the same comparison,
`(omega)/(v)=9.0m^-1`
or `v=(omega)/(9.0m^-1)=(3000s^-1)/(9.0m^-1)=(1000)/(3)(m)/(s)`
The wavelength is
`lamda=(v)/(f)=((1000)/(3(m)/(s)))((3000)/(2piHz))=(2pi)/(9)m`
b. The pressure amplitude is `trianglep_(max)=0.02(N)/(m^2)`. Hence the maximum and minimum pressures at a point in the wave motion will be `1.01xx10^5+-0.02(N)/(m^2)`