A car moving at 20m/s with its horn blowing (f = 1200Hz) is chasing another car going at 15m/s. What is the…

1. Analyze the Question

We are dealing with the Doppler Effect, which describes the change in frequency of a wave in relation to an observer who is moving relative to the wave source.

• Source (Car 1): Moving at $v_s = 20 \, \text{m/s}$, Frequency $f_s = 1200 \, \text{Hz}$.
• Observer (Car 2): Moving at $v_o = 15 \, \text{m/s}$.
• Speed of Sound ($v$): Standard value is $340 \, \text{m/s}$ (unless otherwise specified in the exam).

2. Explain the Concept

The formula for the Doppler Effect is:

• Numerator ($v \pm v_o$): Since the observer is moving away from the source, the frequency decreases, so we use the minus sign ($v - v_o$).
• Denominator ($v \mp v_s$): Since the source is moving towards the observer, the frequency increases, so we use the minus sign ($v - v_s$).

So, the formula becomes:

3. Show the Solution

• $f_s = 1200 \, \text{Hz}$
• $v = 340 \, \text{m/s}$
• $v_o = 15 \, \text{m/s}$
• $v_s = 20 \, \text{m/s}$

Substitute the values into the formula:

Convert to Kilohertz (KHz):

Rounding to two decimal places, we get 1.22 KHz.

4. Identify the Answer

Comparing our result to the options provided, the value matches option A.

5. Tip

Memory Trick: Think of the "Doppler Sign Convention":

• Towards = Increase: If the movement makes the sound pitch higher (closer), the math must result in a larger number.
• Away = Decrease: If the movement makes the sound pitch lower (further), the math must result in a smaller number.
• Always check if the question asks for Hz or KHz to avoid picking the wrong unit (like option D).