Question

A simple harmonic progressive wave is represented as \(Y=0.04\,\sin \pi (2t-0.02x)\) m. At a given instant of time, the phase difference between two particles 10 m apart is (in radian)

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

Hint:

Phase difference is the wave number times the separation.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Write \(Y=0.04\sin(2\pi t-0.02\pi x)\). The coefficient of \(x\) is the wave number \(k=0.02\pi\ \text{rad/m}\).

Step 2: Calculation
At a fixed instant, \(\Delta\phi=k\,\Delta x=0.02\pi\times10=0.2\pi\).

Step 3: Simplify
\(0.2\pi=\dfrac{\pi}{5}\)

Final Answer:
The phase difference is pi over 5 radian. \[ \boxed{\text{(D) }\dfrac{\pi}{5}} \]