a) The wavelength is 5 m
b) The frequency is 0.05 Hz
c) The velocity of the wave is 0.25 m/s
Explanation:
a)
The wavelength of a wave (indicated with the symbol [tex]\lambda[/tex]) is defined as the minimum distance between two points of the wave having the same shape.
So for instance, the wavelength can be measured as the distance between two consecutive crests of the wave, or two consecutive troughs.
In this problem, we have a wave, and we are told that the distance between two crests is :
distance = 5 meters
Therefore, the wavelength corresponds to this distance:
[tex]\lambda = 5 m[/tex]
b)
The frequency of a wave is defined as the number of oscillations of the wave per second: in other words, the frequency of a wave is the number of crests passing a given point every second.
The frequency can be calculated as the reciprocal of the period, where the period is the time that it takes for the wave to do one complete oscillation:
[tex]f=\frac{1}{T}[/tex]
where f is the frequency and T is the period.
For the wave in this problem, we observe that a crest passes a given point every 20 seconds: so, the period of the wave is 20 seconds,
T = 20 s
Therefore, the frequency is:
[tex]f=\frac{1}{T}=\frac{1}{20}=0.05 Hz[/tex]
c)
The velocity of a wave can be calculated using the wave equation:
[tex]v=f \lambda[/tex]
where
v is the velocity of the wave
f is the frequency
[tex]\lambda[/tex] is the wavelength
For the wave in this problem,
[tex]\lambda = 5 m[/tex]
[tex]f=0.05 Hz[/tex]
And substituting,
[tex]v=(5)(0.05)=0.25 m/s[/tex]
Learn more about waves here:
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