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

Answer 1

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