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Question #42053

Difficulty: 8/10 | 🟢 Free

The Question

A stationary source at the origin $x=0$ begins emitting a continuous sound wave of frequency $f_0$ at $t=0$ . The speed of sound in the medium is $c$ . An observer, initially at $x = L$ at $t=0$ , moves along the positive $x$ -axis with a constant velocity $v$ ( $v < c$ ). The observer's equipment is programmed to trigger a light flash exactly after detecting $N$ complete acoustic wave cycles from the source. What is the $x$ -coordinate of the observer when the flash is triggered?

Options

A.
$c \left( \frac{L f_0 + v N}{f_0 (c-v)} \right)$
B.
$\frac{L c}{c-v} + \frac{v N}{f_0}$
C.
$\frac{L c}{c-v} + \frac{N c}{f_0}$
D.
$c \left( \frac{L f_0 + v N}{f_0 (c+v)} \right)$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

The Reaction Time Gap|Frame of Reference|Huygens Principle Wavefronts

Why This Question Is Tricky

Common Mistakes

This question tests the 'Reaction Time Gap' mapped into a coordinate transformation via the Doppler effect.

A common lethal mistake is treating the reaction delay (receiving $N$ cycles) as an absolute time constant $\Delta t = N/f_0$ in the ground frame, ignoring that the observer's motion stretches the effective wavefront arrival time.

Students must realize that the physiological/mechanical delay defined by wave cycles is frame-dependent, requiring the use of the Doppler-shifted frequency $f'$ to find the true time elapsed in the ground frame before the event is triggered.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Straight Line - Class 11 Part 1
Concept	The Reaction Time Gap
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free