Question

A long string is moved up and down with simple harmonic motion with a frequency of 46 Hz. The string is 579 m long and has a total mass of 46.3 kg. The string is under a tension of 3423 and is fixed at both ends. Determine the velocity of the wave on the string. What length of the string, fixed at both ends, would create a third harmonic standing wave

Answer 1

a)
`v=206.896m/s`

b)
`L=6.749m`

Step-by-step explanation:

From the question we are told that:

Frequency
`F=46Hz`

Length
`l=579m`

Total Mass
`T=4.3kg`

Tension
`T=3423`

a)

Generally the equation for velocity is mathematically given by

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

Where

`\pho=m*l\\\\\pho=46*579\\\\\pho=0.0799kg/m`

Therefore

`v=\sqrt{(3423)/(0.0799)}`

`v=206.896m/s`

b)

Generally the equation for length of string is mathematically given by

`L=(3\lambda)/(2)`

Where

`\lambda=(v)/(f)`

`\lambda=(206.89)/(46)`

`\lambda=4.498`

Therefore

`L=(3*4.498)/(2)`

`L=6.749m`