A string of linear density 0.2 kg / m is stretched with a force of 500 N. A transverse wave of

Name: Problem 1476, Chapter 10: JEE Physics
Uploaded: 2021-11-12T17:07:52-08:00
Duration: 1 min 28 s
Channel: Akshaya Rs
Description: A string of linear density 0.2 kg / m is stretched with a force of 500 N. A transverse wave of length 4.0 m and amplitude 1 / 1 meter is travelling along the string. The speed of the wave is …………m / s (A) 50 (B) 62.5 (C) 2500 (D) 12.5

step 1 In this question, we will learn about some basic concept of the oscillation and waves. The quest

Question

A string of linear density $0.2 \mathrm{~kg} / \mathrm{m}$ is stretched with a force of $500 \mathrm{~N}$. A transverse wave of length $4.0 \mathrm{~m}$ and amplitude $1 / 1$ meter is travelling along the string. The speed of the wave is $\ldots \ldots \ldots \ldots \mathrm{m} / \mathrm{s}$ (A) 50 (B) $62.5$ (C) 2500 (D) $12.5$

   A string of linear density $0.2 \mathrm{~kg} / \mathrm{m}$ is stretched with a force of $500 \mathrm{~N}$. A transverse wave of length $4.0 \mathrm{~m}$ and amplitude $1 / 1$ meter is travelling along the string. The speed of the wave is $\ldots \ldots \ldots \ldots \mathrm{m} / \mathrm{s}$
(A) 50
(B) $62.5$
(C) 2500
(D) $12.5$

JEE Physics

StemEZ 1st Edition

Chapter 10, Problem 1476

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Solved by Expert Akshaya Rs

11/12/2021

Step 1

Step 1: The speed of a wave on a string is given by the formula $v = \sqrt{\frac{T}{\mu}}$, where $T$ is the tension in the string and $\mu$ is the linear density of the string. Show more…

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A string of linear density $0.2 \mathrm{~kg} / \mathrm{m}$ is stretched with a force of $500 \mathrm{~N}$. A transverse wave of length $4.0 \mathrm{~m}$ and amplitude $1 / 1$ meter is travelling along the string. The speed of the wave is $\ldots \ldots \ldots \ldots \mathrm{m} / \mathrm{s}$ (A) 50 (B) $62.5$ (C) 2500 (D) $12.5$

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Key Concepts

Wave Speed Formula

The speed of a transverse wave on a string is determined by the formula v = ?(T/?), where T is the tension force and ? is the linear density. This formula illustrates that higher tension increases the wave speed, while higher linear density decreases it, as the wave must move more mass per unit length.

Tension

Tension is the force applied to stretch the string and is a key factor in the propagation of waves. It acts as the restoring force that allows disturbances to travel along the string, and its magnitude directly affects the speed at which the wave travels.

Linear Density

Linear density is the mass per unit length of the string and is crucial in analyzing wave motion. A greater linear density means that there is more mass for the wave to move, which results in slower wave propagation when compared to a string with lower linear density.

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