Question

Consider a stretched string under tension and fixed at both ends. If the tension is

doubled and the cross-sectional area halved, then the frequency becomes:

(A) Twice (C) Four times

(B) Half (D) Eight times
Solve please​

Answer 1

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Asked on December 30, 2019 by

Saule Guda

If the tension in a stretched string fixed at both ends is increased by 21% the fundamental frequency is found to change by 15 Hz. Then the

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ANSWER

Speed of wave in the string isv=

u

T

where T=tension and u = mass per length

So,

fundamental frequencyf=

2L

n

μ

T

where n is the number of harmonics.Number of overtones = (n-1)

Number of nodes = n+1

Number of antinodes = n

fundamental frequency= f=

2L

1

μ

T

Note fundamental wavelength does not change as Length of the string does not change.

Here, T and f varies, new T=1.21T and new f=f +15

so, f+15=1.1f

This gives f=150Hz

so, new velocity=1.1v, which means velocity increases by 10%.