Question

011 10.0 points

A sound wave has a frequency of 634 Hz in air
and a wavelength of 0.47 m.
What is the temperature of the air? As-
sume the velocity of sound at 0°C is 333 m/s.
Answer in units of °C.

Answer 1

`-58.3^(\circ)C`

Step-by-step explanation:

The frequency and the wavelength of a wave are related by the equation

`v=f\lambda`

where

v is the speed

f is the frequency

`\lambda` is the wavelength

For the sound wave in this problem, we have

f = 634 Hz (frequency)

`\lambda=0.47 m` (wavelength)

Therefore, the speed of the wave is

`v=(634)(0.47)=298 m/s`

The speed of sound in air depends on the temperature according to the equation

`v=333+0.6 T`

where T is the temperature.

In this problem, we know the speed, so we can calculate the temperature:

`T=(v-333)/(0.6)=(298-333)/(0.6)=-58.3^(\circ)C`