Question

if sound travels from air to another medium and number of oscillations decrease to fifth for the same distance in air:
-If sound takes 1/3 seconds to move 100 meter in air, find time of the same distance in another medium
- if speed of sound in air equal 300m/sec, find time of sound in the second medium for distance equal 500 meter.

Answer 1

The phrase "number of oscillations decreases to fifth for the same distance in air" means that the number of complete wavelengths in the medium is 5 times smaller than in air.

For air and another medium, we have

$$\lambda_a=5\lambda.$$

Find the speed of sound in air:

$$v_a=100/(1/3)=300\text{ m/s.}$$

Frequency is the same in both media. The 1/3 s in air can be represented as

$$t_a=d/v_a=d/(\lambda_a f).$$

The time for the 100 m in the medium can be written as

$$t=d/v=d/(\lambda f)=5d/(\lambda_a f)=5t_a=5/3\text{ s}.$$

The time for sound to cover 500 m is, therefore, 5 times longer: 25/3 s.