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2 wires of length 78 cm and 80 cm of a s...

2 wires of length 78 cm and 80 cm of a sonometer are kept at the same tension. A tuning fork produces 4 beats per second with each of them . Find out the frequency of the tuning fork .

Text Solution

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Fundamental frequency of the 78 cm long wire,
` n_(1) = (1)/(2 xx 78 )sqrt((T)/(m))`
Fundamental fequency of the 80 cm long wire,
` n_(2) = (1) /(2 xx 80) sqrt((T)/(m))`
`:. (n_(1))/(n_(2)) = (80)/(78), "clearly",n_(1)gtn_(2)`
If n is the frequency of the tuning fork, then
`n_(1) - n = 4 and n - n_(2) = 4 `
`:. n_(1) - n_(2) = 8 "or",(n_(1))/(n_(2)) -1 = (8)/(n_(2))`
or, `(80)/(78) - 1 (8)/(n_(2)) "or",(2)/(78) = (8)/(n_(2)) or , n_(2) = 312 ` Hz .
`:. n = 312 + 4 = 316` Hz .
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