Two identical wires are stretched by the same tension of 100 N and each emits a note of frequen

Name: Problem 107, Chapter 9: A Complete Resource Book in Physics for JEE MAIN
Uploaded: 2021-10-11T13:48:08-08:00
Duration: 2 min 10 s
Channel: Dheeraj Sharma
Description: Two identical wires are stretched by the same tension of 100 N and each emits a note of frequency 200 Hz. If tension in one wire is increased by 1 N, the number of beats heard per second when the wires are plucked is (A) 2 (B) 1 (C) 3 (D) 4

step 1 In this question we have given two identical wires and are stretched by the same tension of 100

Question

Two identical wires are stretched by the same tension of $100 \mathrm{~N}$ and each emits a note of frequency $200 \mathrm{~Hz}$. If tension in one wire is increased by $1 \mathrm{~N}$, the number of beats heard per second when the wires are plucked is (A) 2 (B) 1 (C) 3 (D) 4

   Two identical wires are stretched by the same tension of $100 \mathrm{~N}$ and each emits a note of frequency $200 \mathrm{~Hz}$. If tension in one wire is increased by $1 \mathrm{~N}$, the number of beats heard per second when the wires are plucked is
(A) 2
(B) 1
(C) 3
(D) 4

A Complete Resource Book in Physics for JEE MAIN

Sanjeev Kumar 1st Edition

Chapter 9, Problem 107

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Solved by Expert Dheeraj Sharma

10/11/2021

Step 1

We know that the frequency of a vibrating string is given by the formula: f = (1/2L) * sqrt(T/μ), where L is the length of the string, T is the tension, and μ is the linear mass density of the string. Show more…

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Two identical wires are stretched by the same tension of $100 \mathrm{~N}$ and each emits a note of frequency $200 \mathrm{~Hz}$. If tension in one wire is increased by $1 \mathrm{~N}$, the number of beats heard per second when the wires are plucked is (A) 2 (B) 1 (C) 3 (D) 4

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Key Concepts

Frequency of a Vibrating String

The frequency at which a string vibrates is determined by the tension in the string, its length, and its mass per unit length. Specifically, the frequency is proportional to the square root of the tension, which means that a small change in tension results in a change in the frequency according to a square root relationship.

Beat Frequency

Beat frequency occurs when two waves of slightly different frequencies interfere with each other. It is given by the absolute difference between the two frequencies. In the context of vibrating strings, if one string's tension—and consequently its frequency—is slightly altered, the beat frequency equals the difference between the new frequency and the unchanged frequency.

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