Periodic waves spread out over the surface of a lake where two women, Jenny and Melissa, are fishing in separate boats 65 meters apart. Each woman's boat bobs up and down 19/min. At a time when Jenny's boat is at a crest, Melissa's boat is at its lowest point, and there are 4 additional crests between them. Calculate the wavelength of these water waves.
And what is the speed of these water waves?
To calculate the wavelength of the water waves, we need to determine the distance between a crest and the subsequent crest.
Given that there are 4 additional crests between Jenny's boat and Melissa's boat, this means there are a total of 5 crests between them (including Jenny's crest). Since each boat bobs up and down 19 times per minute, the distance between two consecutive crests is equal to the amplitude of the wave.
Therefore, the wavelength (λ) can be calculated by:
λ = distance between the boats / number of crests
= 65 m / 5
= 13 m
So the wavelength of the water waves is 13 meters.
To calculate the speed of the water waves, we can use the formula:
v = f × λ
where:
v is the speed of the waves,
f is the frequency of the waves (number of crests per second),
and λ is the wavelength.
From the given information, we know that each boat bobs up and down 19 times per minute. To convert this to seconds, we divide by 60:
f = 19 / 60
= 0.3167 Hz
Now we can calculate the speed of the water waves:
v = 0.3167 Hz × 13 m
≈ 4.12 m/s
Therefore, the speed of the water waves is approximately 4.12 meters per second.