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Two cars moving in opposite direction ap...

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

A

350Hz

B

361 Hz

C

411 Hz

D

448Hz

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we will use the Doppler effect formula for sound. The formula to calculate the frequency heard by an observer when the source and observer are moving towards each other is given by: \[ f' = f_0 \frac{v + v_o}{v - v_s} \] Where: - \( f' \) = frequency heard by the observer - \( f_0 \) = frequency of the source (horn) = 400 Hz - \( v \) = velocity of sound in air = 340 m/s - \( v_o \) = velocity of the observer (second car) = 16.5 m/s - \( v_s \) = velocity of the source (first car) = 22 m/s ### Step 1: Identify the values - \( f_0 = 400 \, \text{Hz} \) - \( v = 340 \, \text{m/s} \) - \( v_o = 16.5 \, \text{m/s} \) (since the observer is moving towards the source, we take it as positive) - \( v_s = 22 \, \text{m/s} \) (since the source is moving towards the observer, we take it as positive) ### Step 2: Substitute the values into the formula Now we substitute the values into the Doppler effect formula: \[ f' = 400 \frac{340 + 16.5}{340 - 22} \] ### Step 3: Calculate the numerator and denominator Calculate the numerator: \[ 340 + 16.5 = 356.5 \] Calculate the denominator: \[ 340 - 22 = 318 \] ### Step 4: Substitute back into the formula Now substitute these values back into the formula: \[ f' = 400 \frac{356.5}{318} \] ### Step 5: Perform the division Now calculate the fraction: \[ \frac{356.5}{318} \approx 1.12 \] ### Step 6: Multiply by the frequency of the source Now multiply this by the frequency of the source: \[ f' = 400 \times 1.12 \approx 448 \, \text{Hz} \] ### Conclusion The frequency heard by the driver of the second car is approximately **448 Hz**.
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