The displacement of a particle in a medium is $y=10^{-4} \sin \left[100 t+20 x+\frac{\pi}{3}\right]…
The displacement of a particle in a medium is $y=10^{-4} \sin \left[100 t+20 x+\frac{\pi}{3}\right] \mathrm{m}$, where $t$ is in second and $x$ is in metre. The speed of the wave is
$5 \mathrm{~m} / \mathrm{s}$
$10 \mathrm{~m} / \mathrm{s}$
$15 \mathrm{~m} / \mathrm{s}$
$20 \mathrm{~m} / \mathrm{s}$
Solution
The equation can be written in the form of, $y=y_0 \sin (\omega t+k x+\phi)$ where, $\omega=100 / \mathrm{s}$ and $k=20 / \mathrm{m}$
The velocity of a travelling wave is given by, $v=\omega / k$
Hence, substituting the values, $v=\frac{100}{20}=5 \mathrm{~m} / \mathrm{s}$