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 ...........
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(c)
$v=350 \,m / s \quad f=500 \,Hz$
$v=\frac{\omega}{k}$
$k=\frac{2 \pi f}{v}$
$k=\frac{2 \pi \times 500}{350}$
$k=\frac{2 \pi}{0.7}$
$\therefore \lambda=0.7 \,m$
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 $\approx 3 \pi$
Which is same as $\Delta \phi=\pi$
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