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Frequencies of tuning fork A and B are 258Hz and 262Hz respectively. When A is sounded with a tuning fork `X` of unknown frequency, a beat is produced which is half of the value when B is sounded with X. Unknown frequency is

Frequencies of tuning fork A and B are 258Hz and 262Hz respectively. When A is sounded with a tuning fork `X` of unknown frequency, a beat is produced which is half of the value when B is sounded with X. Unknown frequency is

Grade:11

2 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
one year ago
Dear student

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Arun
25763 Points
one year ago
Here, υA=258Hz,υB=262Hz
Let the frequency of unknown turning fork be υ.
It produces υb beats with A and 2υb with B. Therefore,
υAυ=υb                            ......(i)
and υBυ=2υb                   ......(ii)
Subtract (i) from (ii), we get
υBυA=υb
Substituting the giving values, we get
262258=υb
υb=4Hz
From (i), υ=υAυb=(2584)Hz=254Hz

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