A jetskier is moving at 8.9 m/s in the direction in which the waves on a lake are moving. Each time he passes over a crest, he feels a bump. The bumping frequency is 1.15 Hz, and the crests are separated by 5.8 m. What is the wave speed?
To determine the wave speed, we can use the formula:
Wave speed (v) = frequency (f) × wavelength (λ)
Given:
Bumping frequency (f) = 1.15 Hz
Crest separation (wavelength, λ) = 5.8 m
We need to convert the frequency to angular frequency (ω) since angular frequency is used in the wave speed formula. Angular frequency is given by the formula:
Angular frequency (ω) = 2π × frequency (f)
Using this formula, we can calculate the angular frequency:
ω = 2π × f
= 2π × 1.15 Hz
≈ 7.23 rad/s
Now we can calculate the wave speed using the formula above:
v = ω × λ
= (7.23 rad/s) × (5.8 m)
≈ 41.94 m/s
Therefore, the wave speed is approximately 41.94 m/s.
To find the wave speed, we can use the relationship between wave speed, frequency, and wavelength. The formula is:
wave speed = frequency × wavelength
In this case, we are given the frequency (1.15 Hz) and the distance between the crests (wavelength = 5.8 m). Let's substitute these values into the formula:
wave speed = 1.15 Hz × 5.8 m
Now, we can calculate the wave speed:
wave speed = 6.67 m/s
Therefore, the wave speed is 6.67 m/s.
L = V/F
V = L*F = 5.8 * 1.15 = 6.67 m/s.
Note: The distance between crests is
the wavelength(L).