Question

A wave equation which gives the displacement along the direction is given by $y=0,001\text{ }sin\text{ }(100r+x)$ where, $x$ and y are in metre and $t$ in second. This equation represents a wave

• A. travelling with a velocity of 100 m/s in the negative $x-$ direction
• B. travelling with a velocity of $\frac{50}{\pi }$ m/s in the positive $x-$ direction
• C. of wavelength 1 m
• D. of frequency $\frac{100}{\pi }$ Hz

Answer 1

Answer: (A)

travelling with a velocity of 100 m/s in the negative $x-$ direction

Answer 2

The standard equation of a wave, travelling with amplitude a in the negative $x-$ direction with angular velocity $\omega$ is given by $y=a\sin (\omega t+kx)$ ...(i) where, $k$ is wave number. Given equation of wave is $y=0.001\,\sin (100t+x)$ ..(ii) Comparing Eqs. (i) and (ii), we get $v=\frac{\omega }{k}=\frac{100}{1}$ $=100\,m/s$