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Question

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 length of the strings is


A

1:2

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B

1:3

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C

1:4

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D

1:5

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Solution

The correct option is B

1:3


Step 1: Given parameters

Two uniform strings A and B.

Let,

The frequency of A be n1.

The frequency of B be n2.

Step 2: To find

We have to find the ratio of the length of the strings.

Step 3: Calculation

2n1=3n2

or,

22l1Tm1=32l2Tm2

Here,

m=masslengthm=crosssectionalarea×l×ρlm=crosssectionalarea×ρ

Here,

The cross-sectional area is “a”.

The density of the material is “ρ”.

Now,

l1l2=23m2m1=a2ρa1ρ

Since the density is the same, then

l1l2=23r22r12

By substituting the values, we get

=23122=13

Therefore, option B is the correct choice.


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