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    A longitudinal wave is moving along a spring. Two points on the spring are separated by half a wavelength. The displacements at these points on the spring are always

    A constant
    B in the same direction as each other
    C in the opposite directions to each other
    D in a direction at right angles to the direction of travel of the wave

    C is the answer, but why? I know that half a wavelength is equal to the distance between a compression and a rarefaction on a longitudinal wave, but I can't see how this means the answer is C.

    Thanks for any help.
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    What is the locus described by any point on the spring?

    Draw a sinusoid graph. Place two points half a wavelength apart on the graph (as long as you don't place them at y=0)

    Look at the gradient of each point on the graph. What can you say about the direction of each gradient and hence the direction of travel.

    Move the two points to any other position separated by half a wavelength. Does your answer change?
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    (Original post by uberteknik)
    What is the locus described by any point on the spring?

    Draw a sinusoid graph. Place two points half a wavelength apart on the graph (as long as you don't place them at y=0)

    Look at the gradient of each point on the graph. What can you say about the direction of each gradient and hence the direction of travel.

    Move the two points to any other position separated by half a wavelength. Does your answer change?
    Thanks. The directions of travel are opposite. I understand it now
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    (Original post by uberteknik)
    What is the locus described by any point on the spring?

    Draw a sinusoid graph. Place two points half a wavelength apart on the graph (as long as you don't place them at y=0)

    Look at the gradient of each point on the graph. What can you say about the direction of each gradient and hence the direction of travel.

    Move the two points to any other position separated by half a wavelength. Does your answer change?
    Why is the gradient of a sin graph related to the displacement of a longitudinal wave?? I still don't understand why the answer is C :/
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    (Original post by qwertyuiopg)
    Why is the gradient of a sin graph related to the displacement of a longitudinal wave?? I still don't understand why the answer is C :/
    OK

    It's all about energy transfer:

    Something had to set the wave in motion to start with. i.e. impart kinetic energy to it.

    That original motion in my example is sinusoidal simply because it's easier to imagine the motion. lol!) i.e. a left to right amplitude motion. (normally you picture the sinusoid as a wave moving along the x-time axis left to right, with amplitude on the y-axis up and down. In this example swap the axis. Time is now along the y-axis and amplitude displacement is on the x-axis)

    So when the energy of that motion propagates along the spring, it is replicated by every atom in the spring which vibrates about its starting (equilibrium) position. i.e. also backwards and forwards. In the case of a sine wave, those atoms must also follow the sine wave.

    These animations shows it better than I can describe it:

    http://hermes.ffn.ub.es/~albert/ones/wavemotion.html

    http://youtu.be/7cDAYFTXq3E
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    Thanks!
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    (Original post by qwertyuiopg)
    Thanks!
 
 
 
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