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If the tension in a stretched string fix...

If the tension in a stretched string fixed at both ends is changed by `21%` , the fundamental frequency is found to increase by `15 Hz`, then the

A

original frequency is 150 Hz

B

velocity of propagation of the transverse wave along the string increases by 5%.

C

velocity of propagation of the transverse wave along the string increases by 10% .

D

fundamental wavelength on the string does not change.

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`f prop sqrt T`
`:. f_2/f_1 = sqrt (T_2/T_1)`
`:. (f_1+15)/f_1 = sqrt(1.21T_1)/T_1`
= 1.1
Solving we get `f_1 = 150 Hz`
`v prop sqrtT`
`:. v_2/v_1 = sqrt (T_2/T_1)`
or ` v_2 = sqrt((1.21 T_1)/(T_1)) v_1 `
` = 1.1 v_1`
Hence, increase in v is 10%
`lambda/2 =l `
`:. lambda = 2l `
`:. Fundamental wavelength = 2 lambda is unchanged. `
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Knowledge Check

  • The tension in a stretch string fixed at both ends is changed by 2% , the fundarmental frequency is founder to get changed by 1.5 Hz . Select the correct statement(s).

    A
    Wavelength of the string of fundamental frequency does not change.
    B
    Velocity of propagation of wave changes by 2%.
    C
    Velocity of propagation of wave changes by 1%.
    D
    Original frequency is 1500 Hz.

  • The tension in a stretched string fixed at both ends is changed by 2% , the fundamental frequency is found to get changed by 15Hz . (a) wavelength of the string of fundamental frequency does not change (b) velocity of propagation of wave changes by 2% (c ) velocity of propagation of wave changes by 1% (d) original frequency is 1500Hz

    A
    `c` only correct
    B
    `c` and `d` are correct
    C
    `a,c` and `d` are correct
    D
    `b` and `d` are correct

  • If the tension in a string is increased by 21 percent, the fundamental frequency of the string changes by 15 Hz . Which of the following statements will also be correct?

    A
    The original fundamental frequency is nearly `150 Hz`
    B
    The velocity of propagation changes nearly by `4.5%`
    C
    The velocity of propagation changes nearly by `10%`
    D
    The fundamental wavelength changes nearly by `10%`

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