Two identical sound sources are placed at A and B—one in air and one submerged in water. Class 9

Two identical sound sources are placed at A and B—one in air and one submerged in water. Class 9

Question 1.

Two identical sound sources are placed at A and B—one in air and one submerged in water (Fig). 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? Class 9

Answer:

Let the distance from A (and B) to the cliff = d (same for both).

Time for A (in air) = 2d / v_air

Time for B (in water) = 2d / v_water

Given: Time for A = 4.5 × Time for B

2d/v_air = 4.5 × (2d/v_water)

1/v_air = 4.5/v_water

v_air/v_water = 1/4.5 = 2/9

The ratio of speed of sound in air to water = 1 : 4.5 (or equivalently 2 : 9)