A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. It takes a time of 2.60 for the boat to travel from its highest point to its lowest, a total distance of 0.620 . The fisherman sees that the wave crests are spaced a horizontal distance of 6.40 apar
How fast are the waves traveling?
To find the speed of the wave, we can use the formula for wave speed:
v = λ / T
where:
- v is the wave speed
- λ is the wavelength
- T is the period
Given that the wave crests are spaced 6.40 m apart and it takes 2.60 s for the boat to travel from its highest point to its lowest, we can use these values to find the wave speed.
First, let's calculate the wavelength (λ):
The wave crest spacing is equal to one wavelength, so λ = 6.40 m.
Next, let's calculate the period (T):
The time it takes for the boat to travel from the highest point to the lowest is the period of the wave, so T = 2.60 s.
Now, we can calculate the wave speed (v):
v = λ / T
v = 6.40 m / 2.60 s
Calculating this gives us the wave speed.