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Q.
A sinusoidal wave of frequency $500\, Hz$ has a speed of $350 \,m / s$. The phase difference between two displacements at a certain point at times $1\, m$ apart is
Waves
Solution:
$v=350\, m / s $
$v=\frac{\omega}{k} $
$k=\frac{2 \pi f}{v} $
$k=\frac{2 \pi \times 500}{350} $
$k=\frac{2 \pi}{0.7} $
$\therefore \lambda=0.7 \,m$
Let equation of wave be
$y=A \sin (k x-\omega t)$
Let $x_{1}=0$
$x_{2}=1 m$
$y_{1}=A \sin (\omega t) $
$y_{2}=A \sin \left(\frac{2 \pi}{0.7} \times 1+\omega t\right)$
Hence phase difference $=\frac{20 \pi}{7}$ or approximately
Phase difference $=3 \pi$
Which is same as $\Delta \phi=\pi$