Answer:
7.5 m/s
Explanation:
Standing waves are waves that do not propagate, so they are just oscillations of the medium over fixed positions.
Standing waves are produced for example in a string, which is tied at its ends.
The wavelength of the fundamental mode of vibration of a string is equal to twice the length of the string:
[tex]\lambda=2L[/tex]
where L is the length of the string.
Here, the string vibrates in its fourth harmonic - this means that the wavelength is actually 1/4 of the wavelength of the fundamental mode:
[tex]\lambda_4=\frac{\lambda}{4}[/tex]
Here, the length of the string is
L = 5 m
So the wavelength of the 4th harmonic is:
[tex]\lambda_4=\frac{\lambda}{4}=\frac{2L}{4}=\frac{2(5)}{4}=2.5 m[/tex]
The frequency of the wave is equal instead to the ratio between the number of cycles and the time taken:
[tex]f=\frac{N}{t}[/tex]
where here
N = 48
t = 16 s
Substituting,
[tex]f=\frac{48}{16}=3 Hz[/tex]
Now we can find the string's speed by using the wave equation; we find:
[tex]v=f\lambda=(3 Hz)(2.5 m)=7.5 m/s[/tex]
