What is the fundamental frequency on a 5 m rope that is tied at both ends if the speed of the waves is 24 m/s?

the rope length is one half wavelength, so wavelength= 10 m

freq*wavelenght=speedofwave

To find the fundamental frequency of a rope tied at both ends, we can use the formula:

f = v / λ

where:
f is the frequency,
v is the speed of the waves, and
λ is the wavelength.

To find the wavelength, we need to consider the length of the rope and the node points. For a rope tied at both ends, the fundamental frequency occurs when there is one complete wave between the two ends. This means that the wavelength is twice the length of the rope.

Given that the length of the rope is 5 m, the wavelength (λ) is equal to 2 times 5 m, which gives us a value of 10 m.

Now we can substitute the values into the formula:

f = v / λ
f = 24 m/s / 10 m

Calculating this, we find:

f ≈ 2.4 Hz

Therefore, the fundamental frequency of the rope is approximately 2.4 Hz.