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Question #42092

Difficulty: 8/10 | 🟢 Free

The Question

A transverse sinusoidal wave travels along a taut string of linear mass density $\mu = 0.1 \text{ kg/m}$ in the positive $x$ -direction. The wave propagation speed is $v = 10 \text{ m/s}$ . The maximum transverse acceleration of any particle on the string is $a_{\text{max}} = 200 \text{ m/s}^2$ , and the amplitude of the wave is $A = 2 \text{ cm}$ . What is the time-averaged power $\langle P \rangle$ transmitted by the wave?

Options

A.
2 \text{ W}
B.
50 \text{ W}
C.
0.4 \text{ W}
D.
4 \text{ W}

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

Change in Velocity (Δv)|Particle Velocity vs. Wave Velocity|Energy Density in Transverse Waves

Why This Question Is Tricky

Common Mistakes

This question targets the fundamental distinction between wave propagation velocity and transverse particle velocity.

A common 'Lethal Collision' occurs when students conflate the constant wave speed ( $v$ ) with the oscillating particle speed ( $v_p$ ) when calculating energy density.

By providing the wave speed explicitly, the trap tempts students to incorrectly compute the energy density as $\frac{1}{2}\mu v^2$ (yielding the 50 W trap).

The correct path requires deriving the maximum particle velocity from the given acceleration and amplitude, reinforcing that wave energy transfer is governed by the collective transverse kinetic and potential energies of the medium's particles, not a ballistic translation at the wave speed.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Plane - Class 11 Part 1
Concept	Change in Velocity (Δv)
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free