Question

A 2m long rope is stretched between two supports with a tension that makes the speed of transverse waves 50m/s. What is the wavelength of the fundamental tone?
2m
6m
4m
8m

Answer 1

Answer: 4m

Explanation:

In this situation, while the rope vibrates, a periodic wave travels through it, which is a standing wave.

In this sense, a standing wave has several harmonics  and a fundamental tone (also called fundamental frequency), which is the lowest frequency of this periodic wave and is given by:

$f=\frac{v}{2l}$ (1)

Where:

$f$ is the fundamental frequency

$v=50 m/s$ is the speed of the wave

$l=2 m$ is the longitude of the rope

On the other hand, there is a relation between $l$ and the wavelength $\lambda$ of the fundamental tone:

$l=\frac{\lambda}{2}$ (2)

Finding $\lambda$ from (2):

$\lambda=2l$

$\lambda=2(2 m)$

$\lambda=4 m$ This is the wavelength of the fundamental tone