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20 February, 16:15

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.

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  1. 20 February, 19:34
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    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
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