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: Find the frequency
In medium P: $f = \dfrac{v_P}{\lambda_P} = \dfrac{0.8}{0.15} = 5.33$ Hz.

Step 2: Use it in Q
$v_Q = f\lambda_Q = 5.33\times0.30$.

Step 3: Compute
$v_Q = 1.6$ m/s.

Step 4: Check
The wavelength doubles, so the speed doubles from 0.8 m/s to 1.6 m/s. Options 4.0, 3.2 and 2.0 m/s do not match.

Step 5: Check the other options
The frequency is $\dfrac{0.8}{0.15} = 5.33$ Hz. A speed of 4.0 m/s in Q would need a wavelength of $\frac{4.0}{5.33} = 0.75$ m, and 3.2 m/s would need 0.6 m, and 2.0 m/s would need 0.375 m. None of these is the stated 0.30 m, so only 1.6 m/s fits.

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