string of length 60 cm is suspended from a ceiling the instant a transverse wave pulse is propagated from lower - Physics - Waves

Question

string of length 60 cm is suspended from a ceiling the instant a
transverse wave pulse is propagated from lower end of string A
particle is dropped from the point of suspension distance from
lower end where wave pulse will pass the particle?

Sayantan · Accepted Answer

Dear Student,

Speed of transverse wave:  v=TμMass of the rope can be described as function of distance : m(x)Thus we have m(x)=μxTension T(x)=μgxThus velocity of the pulse  v=gxor,  dxdt=gx   or, dt=dxgxfor Let a Time T the pulse reaches height H∫0Tdt=∫0Hdxgxor T=2HgFor a particle dropping from above, after time T it must be at position H ( as required for them to cross)60-H=12gT2or, 120-2H=4Hor, H=1206⇒H=20 cm
Regards

string of length 60 cm is suspended from a ceiling the instant a transverse wave pulse is propagated from lower end of string A particle is dropped from the point of suspension. distance from lower end where wave pulse will pass the particle?