Question

A body sends a wave \(150\) mm long through medium P and \(0.30\) m long in medium Q. If velocity of the wave in medium P is \(80\,\text{cm s}^{-1}\), the velocity of wave in medium Q is

• A. \(4.0\,\text{m s}^{-1}\)
• B. \(3.2\,\text{m s}^{-1}\)
• C. \(2.0\,\text{m s}^{-1}\)
• D. \(1.6\,\text{m s}^{-1}\)

Hint:

The frequency stays the same in both media, so the speed is proportional to the wavelength.

Answer 1

The Correct Option is D

Step 1: Understand the concept
When a wave passes from one medium into another, its frequency is fixed by the source and does not change. So \(v = f\lambda\) gives \(v \propto \lambda\).

Step 2: Convert units
\(\lambda_P = 150\ \text{mm} = 0.15\) m, \(\lambda_Q = 0.30\) m, and \(v_P = 80\ \text{cm/s} = 0.8\) m/s.

Step 3: Set up the ratio
\[ \frac{v_Q}{v_P} = \frac{\lambda_Q}{\lambda_P} = \frac{0.30}{0.15} = 2 \]

Step 4: Result
\(v_Q = 2\times0.8 = 1.6\) m/s, option (D). The frequency is \(\frac{0.8}{0.15} = 5.33\) Hz in both media.

Final Answer:
The velocity in medium Q is 1.6 m/s. This is option (D). \[ \boxed{\text{(D) }1.6\ \text{m s}^{-1}} \]