A train S₁, moving with a uniform velocity of 108 km/h, approaches another train S₂ standing on a platform. An observer O moves with a uniform velocity of 36 km/h towards S₂, as shown in figure. Both the trains are blowing whistles of same frequency 120 Hz. When O is 600 m away from S₂ and distance between S₁ and S₂ is 800 m, the number of beats heard by O is _______. [Speed of the sound = 330 m s⁻¹]

Question

G1 Physics · Accepted Answer

Step 1: Convert speeds: train S₁ = 30 m s⁻¹, observer = 10 m s⁻¹. Step 2: Apply f' = f(v+vₒ)/(v-vₛ) for S₁ and the corresponding observer-motion formula for stationary S₂. Step 3: Taking the difference of the two received frequencies gives ≈8.125 Hz. Final answer: 8.125.