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

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`

Step-by-step 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{ (T)/(\mu) }`

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

`\mu = (m)/(l)`

substituting values

`\mu = ( 60 *10^(-3))/(2.0 )`

`\mu = 0.03\ kg/m`

So

`v_1 = \sqrt{ (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 )