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A 36cm long sonometer wire vibrates with...

A `36cm` long sonometer wire vibrates with frequency of `280Hz` in fundamental mode, when it is under tension of `24.5N`. Calculate linear density of the material of wire.

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To calculate the linear density of the sonometer wire, we can use the formula for the fundamental frequency of a vibrating string, which is given by: \[ f_0 = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \] Where: - \( f_0 \) is the fundamental frequency (in Hz), ...
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A sonometer wire of length 1 m is stretched by a weight of 10 kg. The fundamental frequency of vibration is 100 Hz. Determine the linear density of material of wire.

A metal wire of diameter 1 mm is held on two knife edges by a distance 50 cm . The tension in the wire is 100 N . The wire vibrating with its fundamental frequency and a vibrating tuning fork together produce 5 beats//s . The tension in the wire is then reduced to 81 N . When the two are excited, beats are heard at the same rate. Calculate (a) frequency of a fork and (b) the density of material of wire.

Knowledge Check

  • A sonometer wire vibrates with frequency n_(1) in air under suitable load of specific gravity sigma . When the load is immersed in water, the frequency of vibration of wire n will be …………… .

    A
    `n_(1) sqrt((sigma +1)/(sigma))`
    B
    `n_(1)sqrt((sigma - 1)/(sigma))`
    C
    `n_(1) sqrt((sigma)/(sigma + 1))`
    D
    `n_(1) sqrt((sigma)/(sigma - 1))`

  • A sonometer wire vibrates with frequency n_1 in air under suitable load of specific gravity sigma . When the load is immersed in water , the frequency of vibration of wire n_2 will be …..

    A
    `n_1sqrt((sigma+1)/(sigma))`
    B
    `n_1sqrt((sigma-1)/(sigma))`
    C
    `n_1sqrt((sigma)/(sigma+1))`
    D
    `n_1sqrt((sigma)/(sigma-1))`

  • A stretched sonometer wire resonates at a frequency of 350 Hz and at the next higher frequency of 420 Hz . The fundamental frequency of this wire is :

    A
    `350 Hz`
    B
    `5 Hz`
    C
    `70 Hz`
    D
    `170 Hz`

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