Question

Two children are sending signals along a cord of total mass 0.45 kg tied between tin cans with a tension of 33 N . It takes the vibrations in the string 0.51 s to go from one child to the other.a. How far apart are the children?b. Express your answer using two significant figures.

Answer 1

`l\approx 19m`

Step-by-step explanation:

Given:

Tension in the string,
`F_T=33N`

mass of the string,
`m=0.45kg`

time taken to transmit the sound,
`t=0.51 s`

We have the relation of the given with velocity 'v' as:

`v^2=(F_T)/(\mu)` ................................(1)

where:

`{\mu}`= linear mass density of the string=
`(m)/(l)`

we know:

`v=(l)/(t)`

where:

`l=`length of the string

Putting the corresponding values in the eq. (1)

`((l)/(t))^2=(F_T)/(((m)/(l)) )`

`l=(F_T* t^2)/(m)`

`\Rightarrow l=(33* 0.51^2)/(0.45)`

`l=19.074\,m`

`l\approx 19m`