Physics(wave motion and propagation)
posted by Kon .
A uniform heavy rope hangs freely from a support. the support is made to oscillate horizontally with a small amplitude so as to send transverse waves down the rope.A standing wave is set up as these waves are reflected at the free end.Which of the following statements is / are correct?
1. the tension is the same throught the rope
2the wavelength is the same throughout the rope
3the frequency of oscillation is the same at all vibrating points of the rope
(please give your explanation of your ans)
If it is hanging freely the tension is highest at the top where the entire weight of the rope is on the hook. The tension at the bottom is zero.
The speed of the wave increases with the square root of tension, and is therefore highest at the top. Therefore the wavelength is short at the top for a given frequency (speed*period = length.
The frequency is the same up and down the rope. There is no way to store waves, the same number per unit time must occur at each point on the rope.