Question

Two vehicles A and B are approaching an observer O at rest with equal speed as shown in the figure. Both vehicles have identical sirens blowing at a frequency $f_s$. The observer hears these sirens at frequency $f_A$ and $f_B$, respectively. Which one of the following is correct? 

• A. $f_A = f_B < f_s$
• B. $f_A = f_B > f_s$
• C. $f_A > f_B > f_s$
• D. $f_A < f_B < f_s$

Hint:

In Doppler problems with angled motion, only the component of velocity toward the observer affects frequency.

Answer 1

The Correct Option is B

Step 1: Using Doppler effect.
When a sound source moves toward a stationary observer, the observed frequency increases. For a source approaching at an angle $\theta$, the effective radial velocity is $v \cos\theta$.

Step 2: Compare frequencies of A and B.
Vehicle A approaches directly along the line of sight, so its radial velocity is maximum. Vehicle B approaches at an angle, so its radial component is smaller. Hence:
$f_A > f_B$.

Step 3: Compare with original frequency.
Since both are approaching, both observed frequencies are greater than the source frequency $f_s$:
$f_A > f_s$ and $f_B > f_s$.

Step 4: Conclusion.
Thus the ordering is $f_A > f_B > f_s$.