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

a)
`f_1 = 2070.6 Hz`

b)
`f_2 = 1929.4 Hz`

Step-by-step explanation:

Apparent frequency of the siren is given as

`f = (v_(rel))/(\lambda)`

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

sowe know

`\lambda = (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 = (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 = (328)/(0.17)`

`f_2 = 1929.4 Hz`