Question

How long is a string under 240 N of tension whose mass is 0.086 kg if a wave travels through it at a speed of 12 m/s?

Answer 1

Answer:

The length of the string is 0.051 meters

Explanation:

It is given that,

Tension in the string, T = 240 N

Mass of the string, m = 0.086 kg

Speed of the wave, v = 12 m/s

The speed of the wave on the string is given by :

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

M is the mass per unit length of the string i.e. M = m/l.......(1)

So, $M=\dfrac{T}{v^2}$

$M=\dfrac{240\ N}{(12\ m/s)^2}$

M = 1.67 kg/m

The length of the string can be calculated using equation (1) :

$l=\dfrac{m}{M}$

$l=\dfrac{0.086\ kg}{1.67\ kg/m}$

l = 0.051 m

So, the length of the string is 0.051 meters. Hence, this is the required solution.