Question

If the string is 7.6 m long, has a mass of 34 g , and is pulled taut with a tension of 15 N, how much time does it take for a wave to travel from one end of the string to the other

Answer 1

The wave takes 0.132 seconds to travel from one end of the string to the other.

Step-by-step explanation:

The velocity of a transversal wave (
`v`) travelling through a string pulled on both ends is determined by this formula:

`v = \sqrt{(T\cdot L)/(m) }`

Where:

`T` - Tension, measured in newtons.

`L` - Length of the string, measured in meters.

`m` - Mass of the string, measured in meters.

Given that
`T = 15\,N`,
`L = 7.6\,m` and
`m = 0.034\,kg`, the velocity of the tranversal wave is:

`v = \sqrt{((15\,N)\cdot (7.6\,m))/(0.034\,kg) }`

`v\approx 57.522\,(m)/(s)`

Since speed of transversal waves through material are constant, the time required (
`\Delta t`) to travel from one end of the string to the other is described by the following kinematic equation:

`\Delta t = (L)/(v)`

If
`L = 7.6\,m` and
`v\approx 57.522\,(m)/(s)`, then:

`\Delta t = (7.6\,m)/(57.522\,(m)/(s) )`

`\Delta t = 0.132\,s`

The wave takes 0.132 seconds to travel from one end of the string to the other.