Question

Two children are sending signals along a cord of total mass 0.56 kg tied between tin cans with a tension of 40 N . It takes the vibrations in the string 0.56 s to go from one child to the other.

Part A How far apart are the children? Express your answer to two significant figures and include the appropriate units.

Answer 1

Velocity of a wave on a string is given by:v= (T/)^0.5 where T is tension and is mass per unit length in the string.

Let the mass of the string be m and its length be d.

So,=m/d.

Hence, velocity = [T/(m/d)]^0.5=(Td/m)^0.5

Now, distance=speed *time

So, for the given problem, d=[(Td/m)^0.5]*t, where t is time.

Hence, (d/t)=(Td/m)^0.5

=>(d/t)^2=Td/m

d=T*(t^2)/m

Here,T=40 N, t=0.56 s, m=0.56 kg.

So, d=40*0.56*0.56/0.56=22.4 m.

So, required distance=22.4 m.