A sound wave of velocity 350 ms-1 is directed towards the surface of water. lf the ratio of the wavelength of sound in water to that in air is 425:100, calc...

A sound wave of velocity 350 ms^-1 is directed towards the surface of water. lf the ratio of the wavelength of sound in water to that in air is 425:100, calculate the velocity on the wave in water

Answer Details

The velocity of a sound wave depends on the properties of the medium through which it is traveling. The formula for the velocity of a sound wave is: v = λf where v is the velocity, λ is the wavelength, and f is the frequency of the wave. In this question, we are given that the velocity of sound in air is 350 ms^-1 and the ratio of the wavelength of sound in water to that in air is 425:100. Let's assume that the frequency of the wave remains constant as it passes from air into water. If the wavelength of the sound wave in air is λ_air, then the wavelength of the same wave in water is: λ_water = (425/100)λ_air = 4.25λ_air Now we can use the formula for the velocity of a sound wave to find the velocity of the wave in water: v_water = λ_waterf Since the frequency of the wave remains constant, we can write: v_water = (4.25λ_air)f We know that the velocity of the wave in air is 350 ms^-1, and we can write: v_air = λ_airf Solving for f, we get: f = v_air/λ_air Substituting this expression for f into the previous equation, we get: v_water = (4.25λ_air)v_air/λ_air Simplifying, we get: v_water = 4.25v_air Substituting the given value for the velocity of sound in air, we get: v_water = 4.25 x 350 ms^-1 Simplifying, we get: v_water = 1487.5 ms^-1 Therefore, the velocity of the wave in water is 1487.5 ms^-1. Option (D) is the correct answer.