011 10.0 points A sound wave has a frequency of 798 Hz in air and a wavelength of 0.48 m. What is the temperature of the a

Question

011 10.0 points
A sound wave has a frequency of 798 Hz in air
and a wavelength of 0.48 m.
What is the temperature of the air? As-
sume the velocity of sound at 0°C is 329 m/s.
Answer in units of °C.
vil

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Thông Đạt 4 years 2021-09-04T05:59:11+00:00 1 Answers 19 views 0

Answers ( )

  1. Ben
    0
    2021-09-04T06:00:55+00:00
    Reply

    The temperature of the air is 66.8° C

    Explanation:

    From the Newton’s  velocity of sound relationship , the velocity of sound is directly proportional to the square root of temperature .

    In this case The velocity of sound = frequency x wavelength

    = 798 x 0.48 = 383 m/sec

    Suppose the temperature at this time = T K

    Thus 383 ∝ \sqrt{T}                       I

    The velocity of sound is 329 m/s at 273 K ( given )

    Thus 329 ∝ \sqrt{273}                   II

    Dividing I by II , we have

    \frac{383}{329} = \sqrt{\frac{T}{273} }

    or \frac{T}{273} = 1.25

    and T = 339.8 K  = 66.8° C

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