Question

Two cars moving in opposite directions approach each other with speed of 22 m/s and 16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is
[velocity of sound 340 m/s]

• A. 350 Hz
• B. 361 Hz
• C. 411 Hz
• D. 448 Hz

Answer 1

The Correct Option is D

To solve this problem, we will use the concept of the Doppler Effect, which is commonly used in sound waves to calculate observed frequencies when both source and observer are in motion.

The formula for the frequency heard by the observer is given by:

f' = f \times \frac{{v + v_o}}{{v - v_s}}

where:

• f' = observed frequency
• f = emitted frequency (400 Hz)
• v = speed of sound (340 m/s)
• v_o = speed of the observer (16.5 m/s)
• v_s = speed of the source (22 m/s)

Both cars are moving towards each other, so the formula will use additive and subtractive velocity correctly:

Inserting the values, we get:

f' = 400 \, \text{Hz} \times \frac{{340 \, \text{m/s} + 16.5 \, \text{m/s}}}{{340 \, \text{m/s} - 22 \, \text{m/s}}}

Calculating the above expression:

• f' = 400 \, \text{Hz} \times \frac{{356.5}}{{318}}
• f' \approx 400 \times 1.121068
• f' \approx 448.43 \, \text{Hz}

Thus, the frequency heard by the driver of the second car is approximately 448 Hz.

Hence, the correct answer is 448 Hz.