A sound wave has a frequency of 628 Hz in air
and a wavelength of 0.49 m.
What is the temperature of the air? Assume the velocity of sound at 0^◦C is 325 m/s.
Answer in units of ◦C.

Answer is 257°C

Explanation:

Given

frequency = 628 Hz

wavelength = 0.49 m

speed of sound at 0°C = 325 m/s

Find

1.speed of sound at t °C=?

2.temperature = ?

Formula

speed of sound at t °C = speed of sound at 0°C   [1+t/273]

Solution

1. speed of sound at t °C = f*∧

                                        = 628*0.49

                                        =307.7m/s

2.speed of sound at t °C = speed of sound at 0°C   [1+t/273]

                    307.7 m/s    = 325 m/s [1+ t/ 273]

                    307.7/325   = 1+t/273

                    0.94             = 1+t/273

              multiplying 273 on both sides

                     (0.94)(273)  = 1+t/273 (273)

                      258             = 1+ t

                       258 - 1        = t

                             257°C    = t

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