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A tuning fork vibrating with sonometre wire of length 20cm produces 5 beats per second . The beat frequency doesn't change if length of wire is changed to 21cm , the frequency of tuning fork is

A tuning fork vibrating with sonometre wire of length 20cm produces 5 beats per second . The beat frequency doesn't change if length of wire is changed to 21cm , the frequency of tuning fork is

Grade:12

2 Answers

Arun
25750 Points
6 years ago
Fundamental frequency is:
n = 1/2l √T/m
n 1/l
assume for 20cm frequency is n1
and for 21 cm frequency is n2
So
n1/n2 = 21/20
then n1 = 21x and n2 = 20x
Let frequency nf for producing 5 beats so n1 > nf > n2
So n1 - nf = 5
21x - nf = 5 ....(i)
And nf - n2 = 5
nf - 20x = 5 .....(ii)
from (1) ans (2) we get x = 205 hz
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

Fundamental frequency is:
n = 1/2l√T/m
n 1/l
assume for 20cm frequency is n1
and for 21 cm frequency is n2
So
n1/n2= 21/20
then n1= 21x and n2= 20x
Let frequency nf for producing 5 beats so n1> nf> n2
So n1- nf= 5
21x - nf= 5 ....(i)
And nf- n2= 5
nf- 20x = 5 .....(ii)
from (1) ans (2) we get x = 205 hz

Thanks and Regards

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