Two identical sound sources are placed at A and B, one in air and one submerged in water as shown in the given figure. Both produce sounds at the same time, which travel horizontally to the vertical side of the cliff and come back. If the time taken by the sound to return to A is 4.5 times than that of B, what is the ratio between the speeds of sound in air and water?

Let the distance travelled by both sounds be the same.

We know that,

$$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$

Since distance is the same, speed is inversely proportional to time.

Given:

$$t_A = 4.5 \ t_B$$

Therefore,

$$\frac{v_{\text{air}}}{v_{\text{water}}} = \frac{t_B}{t_A} = \frac{1}{4.5}$$

$$\frac{v_{\text{air}}}{v_{\text{water}}} = \frac{2}{9}$$

Hence, the ratio between the speeds of sound in air and water is 2 : 9.