To find the frequency of the waves, we need to calculate it using the time it takes for one complete up and down motion of the boat.
Given:
Time period (T) = 2.0 s
Frequency (f) is the reciprocal of the time period, so we can calculate it as:
f = 1 / T
Substituting the value of T:
f = 1 / 2.0 s
f = 0.5 Hz
Therefore, the frequency of the waves is 0.5 Hz.
To find the wavelength of the waves, we can use the length of the boat and the number of wave crests it contains.
Given:
Length of the boat (L) = 3.0 m
In this case, since there are three crests on the boat, the distance covered by three wave crests is equal to the length of the boat. Therefore, the wavelength (λ) is equal to three times the length of the boat.
λ = 3 * L
Substituting the value of L:
λ = 3 * 3.0 m
λ = 9.0 m
Therefore, the wavelength of the waves is 9.0 m.
To find the speed of the waves, we can use the relationship between speed, frequency, and wavelength.
The formula for the speed of a wave is:
v = f * λ
Substituting the values of f and λ:
v = 0.5 Hz * 9.0 m
v = 4.5 m/s
Therefore, the speed of the waves is 4.5 m/s.