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Homework Help: Some specific questions about waves

  1. Jun 1, 2005 #1
    Okay, I have this study guide for a test, but I'm having troubles figuring out the answers...so these are some things I'm wondering:

    1. If you have a taut string, by what factor would you have to increase the tension to double the wave speed?
    I think it's 4, but I'm not sure.

    2. If a string is under constant tension and generates a harmonic wave, by what factor would the amplitude and speed change if the power is doubled?
    I have no clue on this one.

    3. And how would you go about solving this problem: A sinusoidal wave is traveling along a rope. The oscillator that generates the wave completes 40 vibrations in 30s. A given peak travels 5m along the rope in 2s. What is the wavelength?
    I know wavelength equals speed divided by frequency...but I don't know what to use as speed or frequency, so therein lies my problem.

    Any help and/or explanations would be greatly appreciated.
     
  2. jcsd
  3. Jun 2, 2005 #2

    Pyrrhus

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    Homework Helper

    Why don't you try it at the equation so you will be sure?

    [tex] v = \sqrt{\frac{T}{\lambda_{density}} [/tex]

    Example

    [tex] v = \sqrt{\frac{4T}{\lambda_{density}} [/tex]

    [tex] v = 2 \sqrt{\frac{T}{\lambda_{density}} [/tex]

    [tex] v_{new} = 2 v_{old} [/tex]

    What is the definition of frequency????

    frequency = oscilations/time
     
    Last edited: Jun 2, 2005
  4. Jun 2, 2005 #3

    Andrew Mason

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    Use:
    [tex]v = \sqrt{\frac{T}{m/L}}[/tex]

    The energy of a mass, dm, undergoing simple harmonic motion, is proportional to the square of its amplitude. This is apparent, for example, in a mass spring system where the energy of the mass is [itex]\frac{1}{2}kx^2[/itex].
    The power is the time rate of change of energy. So how is the power related to the speed and the square of the amplitude?

    The speed is 2.5 m/sec. The frequency is 80 cps. Solve for wavelength.

    AM
     
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