Question

If the equation of motion of standing waves is $y=0.3 \sin (314\, t-1.57\, x)$, then the velocity of standing wave will be :

• A. 400 m/s
• B. 300 m/s
• C. 200 m/s
• D. 100 m/s

Answer 1

Answer: (C)

200 m/s

Answer 2

Here: Equation of the standing wave is $y=0.3 \sin (314\, t-1.57\, x)$ ...(1) The standard equation of standing wave is $y=a \sin 2 \pi \left[\frac{t}{T}-\frac{x}{\lambda}\right]$ ...(2) Comparing the given equation (1) and standard equation (2), we get $y =0.3 \sin \left[\frac{314 t}{2 \pi}-\frac{1.57}{\lambda}\right]$ $=\frac{0.30}{100} \sin 2 \pi\left(50\, t-\frac{x}{4}\right)$ or $\frac{1}{T}=50$ and $\lambda=4$ Hence, the velocity of the standing wave is $v=n \lambda=\frac{1}{T} \times 4=50 \times 4=200\, m / s$