Physics - Wave on String Question with Solution | TestHub

The given wave equation is $Y=\sin (20\pi x+10\pi t)$.

The oscillating velocity of a particle on the string is given by:

$v=\frac{\partial Y}{\partial t}=10\pi \cos (20\pi x+10\pi t)$

The oscillating speed is the magnitude of the velocity:

$|v|=10\pi |\cos (20\pi x+10\pi t)|$

For two points to have the same oscillating speed at all times, their phase difference must be an integral multiple of $\pi$.

$\Delta \varphi =20\pi \Delta x=n\pi$

For the minimum distance, we take $n=1$:

$20\pi \Delta x=\pi$

$\Delta x=\frac{1}{20}\text{ m}=0.05\text{ m}=5\text{ cm}$

Answer: $5$ cm