Question

The velocity of sound increases by 75% when it enters into a liquid from air
and there is a 25% increase in the wavelength when it enters into another
liquid from the first liquid. The velocity of sound in the second liquid is
_________ if the velocity of sound in 1st liquid is 1100 m s^-1.

• A. 1,275 m s^-1
• B. 1,375 m s^-1
• C. 1,375 cm s^-1
• D. 1,275 cm s^-1

Answer 1

The correct option is B

1,375 m s^-1

Step 1: Given data

The velocity of sound increases by 75% when enters liquid from air.

25% increase in the wavelength when it enters into another
liquid from the first liquid.

Step 2: Solution

So the velocity in liquid 1 is $V\text{'}=V+\frac{3V}{4}=\frac{7v}{4}$

The velocity of sound in 1st liquid is 1100 m s^-1.

$$\begin{gathered} So,\frac{7v}{4}=1100 \\ v=\frac{1100\times 4}{7}=\frac{4400}{7}m{s}^{-1}. \end{gathered}$$

Now the wavelength in liquid 2, $\lambda \text{'}=\lambda +\frac{\lambda }{4}=\frac{5\lambda }{4}$.

In comparing the two solutions,

Velocity in the second medium is 1375 m s^-1.

Hence the correct option is (B).