Question

A 2000 Hz siren and a civil defense official are both at rest with respect to the ground. What frequency does the official hear if the wind is blowing at 12 m/s (a) from source to official and (b) from official to source?

Answer 1

Answer:

a)$f_1 = 2070.6 Hz$

b)$f_2 = 1929.4 Hz$

Explanation:

Apparent frequency of the siren is given as

$f = \frac{v_{rel}}{\lambda}$

as we know that the wavelength will remain the same as it is having originally

sowe know

$\lambda = \frac{340}{2000}$

$\lambda = 0.17 m$

a) Now when wind is blowing from source to official

so we have

$v_{rel} = 340 + 12 = 352 m/s$

so we have

$f_1 = \frac{352}{0.17}$

$f_1 = 2070.6 Hz$

b) Now when wind is from official to source

so we have

$v_{rel} = 340 - 12 = 328 m/s$

so we have

$f_2 = \frac{328}{0.17}$

$f_2 = 1929.4 Hz$