Question

A rope of length L = 5.3 m with a total mass of m = 0.298 kg is tied to a hook rigidly mounted into a wall. A pulse of height 1.4 cm is sent down the rope. The tension in the rope is F = 27 N.

(A) Find the time between sending the pulse down the rope and detecting the pulse that returns.

(B) What is the height of the pulse that returns?

Answer 1

A)

Here we have the velocity of the wave or the pulse generated in the rope,

Here is the tension of the rope

And, is the linear mass density of the rope,ie,mass per unit length.

So,Here total mass of the rope,

Length of the rope,

So,linear mass density,

Tension in the rope,

So, the velocity of the wave or the pulse generated in the rope,

So,when the wave is send down and return back to him,the distance travelled by the wave, is two time the length of the string.

So,

So,the time taken for the sended pulse to come back,

B)

Here the end of the rope is mounted rigidly to the wall,which is a rigid boundary,

So,when we send down a wave to the string,After hitting at the ridi bounday it will change its phase by angle,with the wave equation,,Where the amplitude or the hieght of the wave or pulse is (-A)m which is reversed its direction or now inverted down its value or position.

Here,Here,

So,equation of senn down wave,

Also equation of reflected wave,

Given that the initial Hieght of pulse send down the rope,

So,after reflection hieght of reflected wave or pulse,

So it shows that there is no change in the magnitude of the hieght of the wave ,But as a result of the 180 degree phase change of the reflected wave its direction of amplitude becomes inverted or downwards.(-A),as per the wave equation given above.

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