Question

Please help if you have the time

A string is stretched between fixed supports 2.0 meters apart. When set in transverse vibration at a frequency of 120 Hz the string vibrates in four segments, as shown. What is the wave speed in the string?

Answer 1

We know, length of segment wave is half the wavelength .

Let, wavelength of wave is
`\lambda`.

So, length of segment will be
`(\lambda)/(2)` .

Now, it is given that the string vibrates in four segments.

So,

`L = 4* (\lambda)/(2)\\\\L = 2\lambda\\\\\lambda = 1\ m`

Speed can be given by :

`speed = wavelength * frequency\\\\speed = 1* 120\ m/s\\\\speed = 120\ m/s`

Therefore, the wave speed in the string is 120 m/s.