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:
[tex]f=\frac{v}{2l}[/tex] (1)
Where:
[tex]f[/tex] is the fundamental frequency
[tex]v=50 m/s[/tex] is the speed of the wave
[tex]l=2 m[/tex] is the longitude of the rope
On the other hand, there is a relation between [tex]l[/tex] and the wavelength [tex]\lambda[/tex] of the fundamental tone:
[tex]l=\frac{\lambda}{2}[/tex] (2)
Finding [tex]\lambda[/tex] from (2):
[tex]\lambda=2l[/tex]
[tex]\lambda=2(2 m)[/tex]
[tex]\lambda=4 m[/tex] This is the wavelength of the fundamental tone
