Question

Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow horns having frequency of 676 Hz. The beat frequency heard by each driver will be ______ Hz. [Velocity of sound in air is 340 m/s.]

Hint:

For low speeds $(v \ll c)$, use the approximation $\Delta f \approx f \cdot \frac{2v_{rel}}{c}$. Here $2 \times 676 \times \frac{4}{340} \approx 7.95 \approx 8 \text{ Hz}$.

Answer 1

Correct Answer: 8

Step 1: Speed $v_s = v_o = 7.2 \text{ km/hr} = 7.2 \times \frac{5}{18} = 2 \text{ m/s}$.
Step 2: Frequency heard by one driver from the other car: $f' = f \left( \frac{v + v_o}{v - v_s} \right) = 676 \left( \frac{340 + 2}{340 - 2} \right) = 676 \left( \frac{342}{338} \right)$.
Step 3: $f' = 676 \times 1.01183 \approx 684 \text{ Hz}$.
Step 4: Beat frequency $\Delta f = f' - f = 684 - 676 = 8 \text{ Hz}$.