A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 2.90 s for the boat to travel from its highest point to its lowest, a total distance of 0.640 m. The fisherman sees that the wave crests are spaced 7.60 m apart.
How fast are the waves traveling?
v= x m/s
Isn't the period twice 2.9 seconds?
frequency*wavelength=speed
and freq=1/period
To find the speed of the waves, we first need to calculate the period of the wave, which is the time it takes for one complete cycle.
The boat takes 2.90 s to travel from the highest point to the lowest point, which represents one complete cycle of the wave.
Now we can calculate the frequency of the wave using the formula:
frequency (f) = 1 / period (T)
f = 1 / 2.90 s
Next, we can find the wave speed (v) by multiplying the frequency (f) by the wavelength (λ). The wavelength is the distance between two consecutive wave crests.
v = f * λ
Given that the wave crests are spaced 7.60 m apart, the wavelength (λ) is 7.60 m.
Now, substitute the values into the equation:
v = f * λ
v = (1 / 2.90 s) * 7.60 m
Solving this equation will give us the speed of the waves (v).
To determine the speed at which the waves are traveling, we can use the formula:
v = λ / T
Where:
v is the speed of the waves
λ (lambda) is the wavelength of the waves
T is the time it takes for one complete wave cycle (the period)
In this case, we are given the period T, which is 2.90 s. We need to find the wavelength λ.
The wavelength is the distance between two consecutive wave crests. In this scenario, we are given that the wave crests are spaced 7.60 m apart. However, the distance traveled by the boat from the highest point to the lowest point does not represent the wavelength directly, as it consists of both the upward and downward motion. The total distance traveled by the boat in one complete wave cycle is the wavelength.
To find the wavelength, we can divide the total distance traveled by the boat (0.640 m) by 2, as it covers the distance from the highest point to the lowest point in the given time period.
λ = 0.640 m / 2 = 0.320 m
Now, we can substitute the values into the formula:
v = λ / T
v = 0.320 m / 2.90 s
Calculating this, we find:
v ≈ 0.110 m/s
Therefore, the speed of the waves is approximately 0.110 m/s.