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?

Answer 1

Answer:

Mass of the string, m = 37.7 grams

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, $t=54\ ms=54\times 10^{-3}\ s$

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

$v=\sqrt{\dfrac{T}{\mu}}$

$\mu$ is the mass per unit length, $\mu=\dfrac{m}{l}$

$v=\sqrt{\dfrac{Tl}{m}}$

Also, $v=\dfrac{d}{t}$

$\dfrac{l}{t}=\sqrt{\dfrac{Tl}{m}}$

$m=\dfrac{Tt^2}{l}$

$m=\dfrac{22\times (54\times 10^{-3})^2}{1.7}$

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.