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25 June, 03:06

A sound wave has a frequency of 684 Hz in air and a wavelength of 0.53 m. What is the temperature of the air? Assume the velocity of sound at 0◦C is 327 m/s. Answer in units of ◦C.

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  1. 25 June, 03:28
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    The temperature of air is 335.52 K or 62.52° C

    Explanation:

    First, we calculate the speed of sound wave at the temperature 'T'. We know that:

    v = f λ

    where,

    v = speed of sound at temperature T

    f = frequency of sound at Temperature T = 684 Hz

    λ = wavelength of sound at temperature T = 0.53 m

    Therefore,

    v = (684 Hz) (0.53 m)

    v = 362.52 m/s

    Now, the speed of sound at any temperature, T, is given by the formula:

    V = Vo√ (T/273)

    T = (273) (V² / Vo²)

    where,

    Vo = speed of sound at 0° C = 327 m/s

    Therefore,

    T = (273) (362.52/327) ²

    T = 335.52 K = 62.52° C
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