Question

Equation of a progressive wave is $y=a\sin \left(400\pi t-\frac{\pi x}{0.85}\right),$ then its velocity will be:

• A. 34 m/s
• B. 40 m/s
• C. 340 m/s
• D. 400 m/s

Answer 1

Answer: (C)

Equation of wave is
$y=a\sin \left(400\pi t-\frac{\pi x}{0.85}\right)$
Comparing this equation with
$y=a\sin \left(\omega t-\frac{2\pi x}{\lambda }\right)$
$\omega =400\pi$
$2\pi n=400\pi \Rightarrow n=200$
$\lambda =0.85\times 2=1.7$
Velocity $v=n\lambda =1.7\times 200=340m/s$