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For a stationary wave set up in a string...

For a stationary wave set up in a string having both ends fixed, what is the ratio of the fundamental frequency to the third harmonic?

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Standing Wave Vibrations of string fixed at both ends

Two narrow cylindrical pipes A and B have the same length . Pipe A is open at both ends and is filled with a monoatomic gas of molar mass M_(A) . Pipe B is open at one end and closed at the other end and is filled with a diatomic gas of molar mass M_(B) . Both gases are at the same temperature . a. If the frequency to the second harmonic of the fundamental mode in pipe A is equal to the frequency of the third harmonic of the fundamental mode in pipe B , determine the value of M_(A)//M_(B) . b. Now the open end of pipe B is also closed ( so that pipe B is closed at both ends ). Find the ratio of the fundamental frequency in pipe A to that in pipe B .

Knowledge Check

  • The waves set up in pipes open at both the ends are

    A
    Longitudinal
    B
    Transverse
    C
    Longitudinal stationary
    D
    a and c

  • Four standing wave segments, or loops, are observed on a string fixed at both ends as it vibrates at a frequency of 140 Hz. What is the fundamental frequency of the string?

    A
    23 Hz
    B
    28 Hz
    C
    35 Hz
    D
    47 Hz

  • If you set up the ninth harmonic on a string fixed at both ends, its frequency compared to the seventh harmonic

    A
    Higher
    B
    Lower
    C
    Equal
    D
    None of the above

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    Two narrow cylindrical pipes A and B have the same length. Pipe A is open at both ends and is filled with a monoatomic gas of molar mass M_(A) . Pipe B is open at one end and closed at the other end, and is filled with a distomic gas of molar mass M_(B) . Both gases are at the same tempreture. (a) If the frequency of the second harmonic of the fundamental mode in pipe A is equal to the frequency of the third harmonic of the fundamental mode in pipe B , determine the value of M_(B)//M_(B) . (b) Now the open end of pipe B is also closed (so that the pipe is closed at both ends). Find the ratio of the fundamental frequency in pipe A to that in pipe B .

    The length , radius , tension and density of string A are twice the same parameters of string B . Find the ratio of fundamental frequency of B to the fundamental frequency of A .

    A standing wave is set up in a string of a variable length and tension by a vibrator of variable frequency . Both ends of the string are fixed . When the vibrator has a frequency f , in a string of length L and under tension T , n antinodes are set up in the string is doubled , by what factor should the frequency be changed so that the same number of antinodes is produced? (b) If the frequency and lenght are held constant , what tension will produce n + 1 antinodes ? ( c) If the frequency is tripled and the length of the string is halved , by what factor should the tension be changed so that twice as many antinodes are produced ?

    Two string of same material are stretched to same tension between rigid supports. If diameter of second wire is double than that of first wire and fundamental frequency of first is equal to third harmonic of second wire, find ratio of their lengths.

    The harmonics that accompanied with the fundamental frequency of a vibrating stretched string are

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