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18 August, 06:20

A sound wave with a frequency of 100Hz travels in water with a speed of 1,500 m/s and then travels in air with a speed of 340m/s. Approximately how many time larger is the wavelength in water than in air?

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  1. 18 August, 06:32
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    Answer: 4 times

    Explanation:

    Given that,

    Fequency of sound wave F = 100Hz

    Speed in water Vw = 1,500 m/s

    Speed in air Va = 340m/s

    Wavelength in water (λw) = ?

    Wavelength in air (λa) = ?

    Since wavelength is the distance covered by the wave in one complete cycle, apply the formula V = F λ

    For wavelength in water

    Vw = F x λw

    1500m/s = 100Hz x λw

    λw = 1500m/s / 100Hz

    λw = 150m

    For wavelength in air

    Va = F x λa

    340m/s = 100Hz x λa

    λa = 340m/s / 100Hz

    λa = 34m

    Then, divide λw by λa

    = 150m/34m

    = 4.41 (To the nearest whole number, it is approximately 4)

    Thus, the wavelength in water is 4 times larger than the wavelength in air.
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