Question

A 1.7-m-long string is under 22 N of tension. A pulse travels the length of the string in 54 ms. what is the mass of the string?

Express your answer in grams.

Answer 1

Mass of the string, m = 37.7 grams

Step-by-step explanation:

It is given that,

Length of the string, l = 1.7 m

Tension in the string, T = 22 N

Time taken by the string,
`t=54\ ms=54* 10^(-3)\ s`

The speed in the wave in the string is given by the following formula as :

`v=\sqrt{(T)/(\mu)}`

`\mu` is the mass per unit length,
`\mu=(m)/(l)`

`v=\sqrt{(Tl)/(m)}`

Also,
`v=(d)/(t)`

`(l)/(t)=\sqrt{(Tl)/(m)}`

`m=(Tt^2)/(l)`

`m=(22* (54* 10^(-3))^2)/(1.7)`

m = 0.0377 kg

or

m = 37.7 grams

So, the mass of the strings is 37.7 grams. Hence, this is the required solution.