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The tension, length, diameter and densit...

The tension, length, diameter and density of a string B are double than that of another string A. Which of the following overtones of B is same as the fundamental frequency of A?

A

1st

B

2nd

C

3rd

D

4th

Text Solution

Verified by Experts

The correct Answer is:
C
`eta (v/(2l))_B = (v/(2l))_A`
`eta = sqrt((T//rhoS))/(2l))_B = (v/(2l))_A`
or ` eta ((sqrt (4T//rhopi))/(2ld))_B = ((sqrt(4T//rhopi))/ (2ld))_A` ……….(i)
Given, `T_B = 2T_A, l_B = 2l_A`
d_B = 2d_A`
and `rho_B = 2 rho_A`
Putting in Eq. (i), we get
`eta = 4 `
`eta = 4` means 4th harmonic or 3rd overtone.
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