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The frequency of vibration of a string d...

The frequency of vibration of a string depends of on, (i) tension in the string (ii) mass per unit length of string, (iii) vibrating length of the string. Establish dimensionally the relation for frequency.

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To establish the dimensional relation for the frequency of vibration of a string based on tension (T), mass per unit length (M), and vibrating length (L), we can follow these steps: ### Step 1: Identify the Variables We denote: - Frequency of vibration as \( \nu \) - Tension in the string as \( T \) - Mass per unit length as \( M \) - Vibrating length of the string as \( L \) ...
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The frequency of vibration (v) of a string may depend upon length (I) of the string, tension (T) in the string and mass per unit length (m) of the string. Using the method of dimensions, derive the formula for v.

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Knowledge Check

  • The lowest frequency of the vibrating string is

    A
    Fundamental frequency
    B
    Threshold frequency
    C
    First frequency
    D
    a and b

  • The frequency of vibrations of a stretched string is ________wavelength

    A
    directly 'proportional to
    B
    inversely proportional to
    C
    directly proportional to the square of
    D
    independent of

  • The frequency (n) of vibration of a string is given as n = (1)/( 2 l) sqrt((T)/(m)) , where T is tension and l is the length of vibrating string , then the dimensional formula is

    A
    `[M^(0) L^(1) T^(1)]`
    B
    `[M^(0) L^(0) T^(0)]`
    C
    `[M^(1) L^(-1) T^(0)]`
    D
    `[ML^(0) T^(0)]`

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