Question

11.43--Two children are sending signals along a cord of total mass 0.44 kg tied between tin cans with a tension of 33 N . It takes the vibrations in the string 0.59 s to go from one child to the other. How far apart are the children?

Answer 1

The speed c of the elastic wave is given by,

c = √(T/μ)

where T is the tension and μ is the linear density of the cord.

T = 33 N ; μ = m/L . Then ,

c = √( T* L/m).

Δx = L ...[distance between the two children]

L = c*t

L = √(T*L/m) * t

squaring on both sides,

L^2 = (T*L/m) * t^2
L = (T/m)*t^2

now putting the values,

L = (33/0.44) * 0.59^2

L = 26.105 m

so, the children are 26.105 m apart.