A stationary source is emitting sound at a fixed frequency f₀ , which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is 1.2 % of f₀ . What is the difference in the speeds of the cars (in km per hour) to the nearest integer ? The cars are moving at constant speeds much smaller than the speed of sound which is 330 ~ms ⁻¹ .

Step-by-step solution

Firstly, car will be treated as an observer which is approaching the source. Then, it will be treated as a source, which is moving in the direction of sound. Hence, f₁=f₀ ( v+v₁ v-v₁ ) aligned f₂ & =f₀ ( v+v₂ v-v₂ ) f₁-f₂ & = ( 1.2 100 ) f₀ & =f₀ [ v+v₁ v-v₁ - v+v₂ v-v₂ ] or ( 1.2 100 ) f₀ & = 2 v (v₁-v₂ ) (v-v₁ ) (v-v₂ ) f₀ aligned As v₁ and v₂ are very very less than v . We can write, (v-v₁ ) or (v-v₂ ) v ( 1.2 100 ) f₀= 2 (v₁-v₂ ) v f₀ or (v₁-v₂ )= v 1.2 200 aligned & = 330 1.2 200 =1.98 ~ms ⁻¹ & =7.128 kmh ⁻¹ a