Questions

If  are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by

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a
1n=1n1+1n2+1n3
b
1n=1n1+1n2+1n3
c
n=n1+n2+n3
d
n=n1+n2+n3

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detailed solution

Correct option is A

n1=12l1Tμ                       . . . .  (i)n2=12l2Tμ                               . . . . .(ii)n3=12l3Tμ                          . . . . . (iii) andn=12lTμ                        . . . . . (iv) From eqn. (iv), we get 1n=2lTμ As l=l1+l2+l3∴  1n=2l1+l2+l3Tμ=2l1Tμ+2l2Tμ+2l3Tμ=1n1+1n2+1n3 (using (i), (ii) and (iii))

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In Melde’s experiments in the longitudinal mode of vibration a string vibrates in 4 loops with a load of 8 gm. How much load would be required in order that the string many vibrate in 8 loops in transverse mode.

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