Question #164236

A car travelling at 10ms-1 sounds its horn, which has a frequency of 500 Hz, and this is heard in

      another car which is travelling behind the first car, in the opposite direction, with a velocity of

      20ms-1. The sound can also be heard in the second car by reflection from a bridge ahead, in the

      direction of the first car. What frequencies will the driver in the second car hear?


1
Expert's answer
2021-03-12T07:15:13-0500

(a)Let's first find the frequency that the driver in the second car hear when the sound of the horn is directly coming to the second car:


fo=fs(vvov+vs),f_o=f_s(\dfrac{v-v_o}{v+v_s}),fo=500 Hz(340 ms20 ms340 ms+10 ms)=457 Hz.f_o=500\ Hz\cdot(\dfrac{340\ \dfrac{m}{s}-20\ \dfrac{m}{s}}{340\ \dfrac{m}{s}+10\ \dfrac{m}{s}})=457\ Hz.

(b) Let's first calculate the frequency at the bridge:


fo,b=fs(vvvs),f_{o,b}=f_s(\dfrac{v}{v-v_s}),fo,b=500 Hz(340 ms340 ms10 ms)=515.1 Hz.f_{o,b}=500\ Hz\cdot(\dfrac{340\ \dfrac{m}{s}}{340\ \dfrac{m}{s}-10\ \dfrac{m}{s}})=515.1\ Hz.

Finally, we can find the frequency of the reflected sound:


fo,r=fs,b(vvovvs),f_{o,r}=f_{s,b}(\dfrac{v-v_o}{v-v_s}),fo=515.1 Hz(340 ms20 ms340 ms10 ms)=500 Hz.f_o=515.1\ Hz\cdot(\dfrac{340\ \dfrac{m}{s}-20\ \dfrac{m}{s}}{340\ \dfrac{m}{s}-10\ \dfrac{m}{s}})=500\ Hz.

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