Question

A sinusoidal wave of frequency 500 Hz has a speed of 350 m/s. How far apart are two points that differ in phase by Tn answer in cmm ad? Give yo Sample submission: 12.3 Not for credit: you may also calculate the phase difference between two displacements at a certain point at times 1.00 ms apart.

Answer 1

We know that the velocity of a sinusoidal wave in terms of frequency and wavelength is given by $v=f\lambda$.

In this case,$\lambda =v/f=(350 m/s)/500Hz=0.7 m.$

This means that for a phase difference of $2\pi$ rad, the distance between any 2 points on the wave is 0.7 m=70 cm.

Hence for a phase difference of $\pi /3$ rad, the distance is $(70*\pi /3)/2\pi =70/6=11.7 cm.$

Also the phase difference at a certain point at times 1m s apart=$\omega *10^{-3}=2\pi f*10^{-3}=1000\pi *10^{-3}=\pi$ rad.