Question

Sound in water travels at a velocity governed by the relation v = √(B/rho) where B is the bulk modulus and rho is the density. For salt water, take B = 2.28 × 109 Pa and rho = 1043 kg/m3. A whale sends out a high frequency (10 kHz) song to another whale 1.0 km away.

Answer 1

Answer:

t = 0.67635 s

n = 6764

Explanation:

Given:

- The velocity of sound in water v:

                                    v = √(B/rho)

Where, B: Bulk Modulus = 2.28*10^9 Pa

            rho: Density of salt water = 1043 kg/m^3

- The wale sends out a high frequency f = 10 kHz

- The distance between two wales s = 1.0 km

Find:

- Time taken for the sound to travel between whales t?

- How many wavelengths can fit between the two whales n?

Solution:

- The time taken for the sound to travel from one whale to another can be determined from:

                               t = s / v

                               t = s / √(B/rho)

                               t = s*√(rho/B)

- Plug in the values:

                               t = 1000*√(1043/2.28*10^9)

                              t = 0.67635 s

- The wavelength λ of the sound emitted can be calculated by the following formula:

                               λ = √(B/rho) / f

                               λ = √(2.28*10^9/1043) / 10^4

                               λ =  0.14785 m

- The number of wavelengths n that could fit in the distance s is:

                               n*λ = s

                               n = 1000 / 0.14785

                              n = 6764