The Question is from neet-physics waves speed-of-a-transverse-wave, and it was created by the author Mr. ANIL KUMAR.G

Question

A stretched string of length L and mass m is under tension T. If a small transverse pulse is generated at one end, and another pulse, identical in shape but inverted, is generated at the other end simultaneously, at what time will the two pulses completely neutralize each other? Assume the pulses do not undergo any reflection.

Mr. ANIL KUMAR.G · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
	**Primary Concept**: Wave Propagation on a String
	**Related Topics**: Wave Interference, Wave Speed
	**Prerequisites**: Understanding of wave speed, superposition principle, and wave interference.
## SOLUTION PATHWAY
**Given Information**:
	* String Length: L
	* String Mass: m
	* Tension: T
	* Two identical but inverted pulses are generated at opposite ends simultaneously.
**Method & Steps**:
	1. Determine the speed of the pulses on the string.
		Reasoning: The speed of a transverse wave on a string depends on the tension and the linear mass density (mass per unit length).
		Formula/Rule: $v = \sqrt{\frac{T}{\mu}}$, where $\mu = \frac{m}{L}$ is the linear mass density.
	2. Calculate the time for each pulse to travel half the length of the string.
		Working: The pulses will meet and neutralize each other at the center of the string.  Thus, each pulse needs to travel a distance of L/2.
		Key Point: Since the pulses start simultaneously, they will meet and cancel out when each has traveled half the length of the string.
	3. Find the time using the distance and speed.
		Result: $t = \frac{	ext{distance}}{	ext{speed}} = \frac{L/2}{\sqrt{\frac{T}{m/L}}} = \frac{L}{2}\sqrt{\frac{m}{TL}} = \frac{1}{2}\sqrt{\frac{mL}{TL}} = \frac{1}{2}\sqrt{\frac{m}{T}}$
		Verification: The units of the result are $\sqrt{\frac{kg}{N}} = \sqrt{\frac{kg}{kg\cdot m/s^2}} = \sqrt{\frac{s^2}{m^2}} = s$, which is the unit of time.
 ## OPTION ANALYSIS
[A] :x: $t = L\sqrt{\frac{m}{T}}$: This represents the time for a pulse to travel the entire length of the string, not half the length.
[B] ✓: $t = \frac{1}{2}\sqrt{\frac{m}{T}}$: This is the correct answer, as derived above. It represents the time for each pulse to travel half the length of the string.
[C] :x: $t = 2L\sqrt{\frac{m}{T}}$: This corresponds to the time for a pulse to travel twice the length of the string, which is not relevant to this problem.
[D] :x: $t = \frac{1}{4}\sqrt{\frac{m}{T}}$: This is a quarter of the time needed for a pulse to travel the entire length, which is also incorrect.
 ## LEARNING AIDS
	**Common Mistakes**:
		1. Using the total length L instead of L/2: Remember that the pulses meet in the middle.
		2. Confusing the formula for wave speed: Make sure to use the correct formula $v = \sqrt{\frac{T}{\mu}}$.
	**Quick Tips**:
		1. Visualize the pulses traveling towards each other to understand why they meet at the center.
		2. Remember the relationship between speed, distance, and time: $	ext{time} = \frac{	ext{distance}}{	ext{speed}}$.

Mr. ANIL KUMAR.G · Answer

t = L*sqrt(m/T)

Mr. ANIL KUMAR.G · Answer

The correct Option is "t = (1/2)sqrt(m/T)"

Mr. ANIL KUMAR.G · Answer

t = 2L*sqrt(m/T)

Mr. ANIL KUMAR.G · Answer

t = (1/4)sqrt(m/T)

NEET Physics Waves Speed Of A Transverse Wave MCQs

Select Topic

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

Question Tags

NEET Subjects

Our Bots

Company