Speed of transverse string waves

[babykeys23]

A piano string of length 1.5 m and mass density 25mg/m vibrates at a (fundamental) frequency of 460 Hz.
What is the speed of the transverse string waves?


v=sqrt (FL/m)

v= sqrt (37.5*1.5/25)

is this the right track?

 

[G01]

I would try using the equation:

$$v=\lambda f$$

You know f already. All you need then, is the wavelength,$$\lambda$$. You know the wave is vibrating at a fundamental frequency. Does this tell you anything about the wavelength of that wave?

 

[ogb p]

Yes, that is the correct equation to use to calculate the speed of transverse string waves. However, the units may need to be converted to be consistent. The mass density is given in milligrams per meter, so it needs to be converted to kilograms per meter in order to be consistent with the other units. The final result should be in meters per second (m/s). So the correct calculation would be:

v= sqrt ((37.5*1.5)/0.025) = 34.64 m/s

Therefore, the speed of the transverse string waves in this scenario is approximately 34.64 meters per second.