Question

A sound wave has a frequency of 662 hz in air and a wavelength of 0.54 m. what is the temperature of the air? relate the speed of sound in air to temper-sture in units of kelvin, but answer in unite of celsius. assume the velocity of sound at 0°c is 330 m/s. answer in units of dego.

Answer 1

The speed of sound in air can be determined using the formula:

v = fλ

where v is the speed of sound, f is the frequency, and λ is the wavelength.

Substituting the given values, we get:

v = (662 Hz)(0.54 m) = 357.48 m/s

We can then use the formula relating the speed of sound in air to temperature:

v = 331.3 + 0.606T

where v is the speed of sound in m/s and T is the temperature in Celsius.

Solving for T, we get:

T = (v - 331.3) / 0.606 = (357.48 - 331.3) / 0.606 = 43.11°C

Therefore, the temperature of the air is approximately 43.11°C.