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Questions  

 Two uniform strings, A and B made of steel are made to vibrate under the same tension. Radius of A is two times the radius of B . If the first overtone of A is equal to the second overtone of B, the ratio of lengths of the string is

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a
1 :2
b
1 :3
c
1:4
d
1:5

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detailed solution

Correct option is B

Given that first overtone of string A is equal to second overtone of string 8. Thus the second harmonic of A is equal to third harmonic of B, i.e.,   or 21LArATπρ=31LBrBTπρ or 21LArATρ=31LBrBTρ or 2LArA=3LBrB or LALB=2rB3rA=2rB32rB or LALB=13  or  LA:LB=1:3

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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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