Two identical wires are stretched by the same tension of 100N and each emits a note of frequency 200 cycles s–1. The tension in one wire is increased by 1 N. Find the number of beats heard per second when the wires are plucked simultaneously.

Engineering

Physics

Approximation and Order of Magnitude

Interference of Sound Wave

Standing Wave on String

Question

Two identical wires are stretched by the same tension of 100N and each emits a note of frequency 200 cycles s^–1. The tension in one wire is increased by 1 N. Find the number of beats heard per second when the wires are plucked simultaneously.

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Frequency of fundametal note emitted by each axis before the tension change occurs is

$F = \frac{1}{2 L} {(\frac{T}{µ})}^{1 / 2}$ .....(1)

$\frac{δF}{δT} = \frac{1}{2 L} (\frac{1}{2} {(\frac{T}{µ})}^{- \frac{1}{2}} \frac{1}{µ}) = \frac{1}{4 LT} {(\frac{Τ}{µ})}^{1 / 2}$ .....(2)

From equation (i) & (ii)

$\frac{df}{dT} = \frac{f}{2 T}$

$= ΔF = \frac{f}{2} \frac{ΔT}{T}$

$ΔF = (\frac{200}{2}) (\frac{1}{100})$

( $∴$ DF = Beat frequency)

= 1 cycle s^–1