Question

Assume the speed of sound in air to be v = 344 m/s. The siren of a fire engine that is driving northward at 30.0 m/s emits a sound of frequency 2000 Hz. A truck in front of this fire engine is moving northward at 20.0 m>s. (a) What is the frequency of the siren’s sound that the fire engine’s driver hears reflected from the back of the truck? (b) What wavelength would this driver measure for these reflected sound waves?

Answer 1

2120.38915 Hz

0.17638 m

Step-by-step explanation:

`f_s` = Frequency of sound emitted by the engine = 2000 Hz

`v_t` = Speed of truck = 20 m/s

`v_s` = Speed of fire engine = 30 m/s

v = Speed of sound in air = 344 m/s

Frequency of the fire engine is given by

`f_t=f_s(v-v_t)/(v-v_s)\\\Rightarrow f_t=2000(344-20)/(344-30)\\\Rightarrow f_t=2063.69426\ Hz`

The frequency of the fire engine that is heard is 2063.69426 Hz

For the engine

`f_e=f_t(v+v_s)/(v-v_t)\\\Rightarrow f_e=2063.69426(344+30)/(344+20)\\\Rightarrow f_e=2120.38915\ Hz`

The frequency that the fire engine's driver hears reflected from the back of the truck is 2120.38915 Hz

Wavelength is given by

`\lambda=(v+v_s)/(f_t)\\\Rightarrow \lambda=(344+20)/(2063.69426)\\\Rightarrow \lambda=0.17638\ m`

The wavelength would be 0.17638 m