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  4. A progressive wave of frequency 500 Hz is travelling with a velocity of 360 m /s How far apart are two points 60° out of phase ?

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Q. A progressive wave of frequency 500 Hz is travelling with a velocity of $360\, m /s$ How far apart are two points $60^{\circ}$ out of phase ?

Waves

Solution:

For a wave, velocity $v=v \lambda$
$\therefore \lambda=\frac{v}{v}=\frac{360}{500}=0.72\, m$
Phase difference, $\Delta \phi=\frac{2 \pi}{\lambda} \times($ Path difference $\Delta x$ )
Phase difference, $\Delta \phi=60^{\circ}=\left(\frac{\pi}{180}\right) \times 60=\left(\frac{\pi}{3}\right)$ rad
So path difference, $\Delta x=\frac{\lambda}{2 \pi}(\Delta \phi)=\frac{0.72}{2 \pi} \times \frac{\pi}{3}=0.12\, m$