wiz-icon
MyQuestionIcon
MyQuestionIcon
3
You visited us 3 times! Enjoying our articles? Unlock Full Access!
Question

A uniform rope of mass m and length L hangs from a ceiling. (a) Show that the speed of a transverse wave on the rope is a function of y, the distance from the lower end, and is given by v=gy. (b) Show that the time a transverse wave takes to travel the length of the rope is given by t=2L/g.

Open in App
Solution

we know, The wave speed at any point on the string is given by the equation
v=τμ
where: τ is not the tension along the whole string, it is the tension at the point where the speed need to be find but since we are usually dealing with uniform strings or ropes then τ is given for the whole string also,because in most cases the string is lying horizontally
we can write the tension as follows
τ=mLgy=μgy
By substitution to find the wave speed we have
v=μgyμ=gy
b) For the second part, the time taken by the wave to travel from one end to the other end of the rope will be dt=Lv and we noticed that we have used the differential representation for time because the speed v is not the speed along the whole rope it is the speed at a particular point y So now we need to integrate over y to find t
T=L0dt=L0Lgy=2Lg

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Dimensional Analysis
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon