When the observer moves towards a stationary source with velocity V₁ , the apparent frequency of emitted note is F₁ . When observer moves away from the source with velocity V₁ , the apparent frequency is F₂ . If V is the velocity of sound in air and F₁ / F₂=2 then V / V₁ is equal to

Step-by-step solution

Apparent frequency shifts occur due to the Doppler effect when an observer moves relative to a stationary sound source. When the observer approaches the source with velocity v₁ , the apparent frequency is F₁ = F ( V + v₁ V ) . When moving away, the apparent frequency becomes F₂ = F ( V - v₁ V ) . Given that F₁ F₂ = 2 , the ratio simplifies to F₁ F₂ = V + v₁ V - v₁ = 2 . Solving for V v₁ : 2(V - v₁) = V + v₁ 2V - 2v₁ = V + v₁ V = 3v₁ V v₁ = 3 . The ratio of the speed of sound to the observer's speed is 3 .