Question

A string of mass 60.0 g and length 2.0 m is fixed at both ends and with 500 N in tension. a. If a wave is sent along this string, what will be the wave's speed? A second wave is sent in the string, what is the new speed of each of the two waves?

Answer 1

Answer:

a

The  speed of  wave is   $v_1 = 129.1 \ m/s$

b

The new speed of the two waves is $v = 129.1 \ m/s$

Explanation:

From the question we are told that

    The mass of the string is  $m = 60 \ g = 60 *10^{-3} \ kg$

    The length is  $l = 2.0 \ m$

    The tension is  $T = 500 \ N$

Now the velocity of the first wave is mathematically represented as

     $v_1 = \sqrt{ \frac{T}{\mu} }$

Where  $\mu$ is the linear density which is mathematically represented as

      $\mu = \frac{m}{l}$

substituting values    

     $\mu = \frac{ 60 *10^{-3}}{2.0 }$

     $\mu = 0.03\ kg/m$

So

   $v_1 = \sqrt{ \frac{500}{0.03} }$

   $v_1 = 129.1 \ m/s$

Now given that the Tension, mass and length are constant the velocity of the second wave will same as that of first wave (reference PHYS 1100 )