Question

. A convertible moves toward you and then passes you; all the while, its loudspeakers are producing a sound. The speed of the car is a constant 9.30 m/s, and the speed of sound is 342 m/s. What is the ratio of the frequency you hear while the car is approaching to the frequency you hear while the car is moving away

Answer 1

`1.056`

Step-by-step explanation:

v = Velocity of sound = 342 m/s

`v_s` = Velocity of source of sound = 9.3 m/s

`f_a` = Frequency when car is approaching

`f_m` = Frequency when car is moving away

`f_s` = Frequecy of source of sound

The required ratio is

`(f_a)/(f_m)=((v)/(v-v_s)f_s)/((v)/(v+v_s)f_s)\\\Rightarrow (f_a)/(f_m)=(v+v_s)/(v-v_s)\\\Rightarrow (f_a)/(f_m)=(342+9.3)/(342-9.3)\\\Rightarrow (f_a)/(f_m)=1.056`

The ratio of the frequency you hear while the car is approaching to the frequency you hear while the car is moving away is
`1.056`