What is the velocity and frequency of the waves traveling on the rope?

pantera_3_27 asked:


A rope of length 3.8 meters has a mass of 1.2 kilograms. The rope is stretched so that the tension in the rope is 3.0 Newtons, and waves of wavelength 5.4 meters are seen traveling along the rope.

What is the velocity of the waves traveling on the rope?
What is the frequency of the waves on the rope?

zerachia

Comments (1)

  1. hfshaw says:
    October 24, 2009 at 3:55 am

    The phase velocity (the speed of a wave with a specific frequency or wavelength) on a string with linear mass density D and tension T is given by:

    v = sqrt(T/D)

    In this case, the linnear mass density is:

    D = 1.2 kg / 3.8 m = 0.316 kg/m

    The phase velocity if the tension is 3.0 N is then:

    v = sqrt((3 N)/(0.316 kg/m))

    v = 3.1 m/s

    The frequency and wavelength of any wave of a specified frequency are related by:

    v = frequency * wavelength

    so the wave in this problem would have a frequency of;

    frequency = v/wavelength = (3.1 m/s)/(5.4 m)

    frequency = 0.57 Hz