Physics - Wave on String Question with Solution | TestHub

The given wave equation is $y=0.2\sin 4\pi \left[\frac{t}{0.08}+\frac{x}{0.8}+\frac{1}{12}\right]$

Comparing this with the standard wave equation $y=A\sin (\omega t+kx+\varphi )$

$\omega =\frac{4\pi }{0.08}=50\pi$ rad/s

$k=\frac{4\pi }{0.8}=5\pi$ rad/m

Since the signs of $\omega t$ and $kx$ are the same, the wave is traveling in the negative x-direction.

The velocity of the wave is $v=\frac{\omega }{k}=\frac{50\pi }{5\pi }=10$ m/s

The wavelength is $\lambda =\frac{2\pi }{k}=\frac{2\pi }{5\pi }=0.4$ m

Answer: negative x-direction with velocity 10 m/s and with wavelength 0.4 m.