Question

A transverse wave is described by the equation \(y=A\sin 2\pi \left(nt-\frac{x}{10}\right)\). The ratio of maximum particle velocity to wave velocity is

• A. \(\frac{\pi A}{5}\)
• B. \(\frac{2\pi A}{5}\)
• C. \(\frac{3\pi A}{5}\)
• D. \(\frac{4\pi A}{5}\)

Hint:

Compare the wave equation with the standard form to get the angular frequency and wavelength, then find the maximum particle speed and wave speed.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Compare with \(y=A\sin2\pi\left(nt-\frac{x}{\lambda}\right)\): the frequency is \(n\) and the wavelength is \(\lambda=10\).

Step 2: Calculation
Maximum particle velocity \(=A\omega=2\pi nA\). Wave velocity \(v=n\lambda=10n\).

Step 3: Ratio
\(\frac{v_{max}}{v}=\frac{2\pi nA}{10n}=\frac{\pi A}{5}\).

Final Answer:
The ratio is pi A divided by 5. \[ \boxed{\text{(A) }\dfrac{\pi A}{5}} \]