Answer to Question #283288 in Physics for Akaye

Question

An object explodes and its sound wave propagates through the sea where the temperature is 37 C. It also propagates through air with a 30°C temperature. What will be the difference in the arrival time between the two signals at a station that in 75 km away? (bulk modulus of seawater - 3x10 N/m: seawater density-1245 kg/m³; molar mass of air is .049 kg)

Answer 1

Speed of sound in water:

$$c_w=\sqrt\dfrac{B}{\rho_w}=1552\text{ m/s}.$$

Speed of sound in air:

$$c_a=\sqrt\dfrac{\gamma RT}{M}=271\text { m/s}.$$

The difference in times of arrival:

$$\Delta t=d\bigg(\dfrac1{c_a}-\dfrac1{c_w}\bigg)=228\text{ s}.$$