Q.

Two uniform strings A and B made of steel are made to vibrate under the same tension. if the first overtone of A is equal to the second overtone of B and if the radius of A is twice that of B, the ratio of the lengths of the strings is

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a

1 : 2

b

1 : 3

c

1 : 4

d

1 : 6

answer is B.

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Detailed Solution

First overtone of string A = Second overtone of string B.⇒Second harmonic of  A = Third harmonic of B⇒n2=n3⇒2(n1)A=3(n1)B  (∵n1=12lTπr2ρ)⇒2 12lArATπρ=3 12lBrBTπρ lAlB=23rBrA⇒lAlB=23×rB(2rB)=13
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Two uniform strings A and B made of steel are made to vibrate under the same tension. if the first overtone of A is equal to the second overtone of B and if the radius of A is twice that of B, the ratio of the lengths of the strings is