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