Question

It takes 3s for a sound wave to travel to a point 1km above the water surface from its source which is
kept under the water at a depth of hm. Determine the value of h, if it is given that velocity of sound in air
is 340ms-1
and in water is 1420ms-1

Answer 1

Answer on Question #50141, Physics, Mechanics | Kinematics | Dynamics

It takes 3s for a sound wave to travel to a point 1km above the water surface from its source which is kept under the water at a depth of h m. Determine the value of h, if it is given that velocity of sound in air is 340 ms⁻¹ and in water is 1420 ms⁻¹.

Solution:

The time of travel is

$$t = t_1 + t_2 = 3 \text{ s}$$

where $t_1$ and $t_2$ are times of travel in water and air, respectively.

$$t_1 = h / v_{\text{water}}$$ $$t_2 = \frac{d}{v_{\text{air}}} = \frac{1000 \text{ m}}{340 \text{ m/s}}$$

Thus,

$$\frac{h}{v_{\text{water}}} + \frac{d}{v_{\text{air}}} = t$$

Hence,

$$h = v_{\text{water}} \left(t - \frac{d}{v_{\text{air}}}\right) = 1420 * \left(3 - \frac{1000}{340}\right) = \frac{1420}{17} = 83.5 \text{ m}$$

Answer: $h = 83.5 \text{ m}$

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