A woman is sitting in a boat at anchor on a lake. Her boat bobs up and down once every 2.0·s. She notices that when the front of her 3.0·m long boat is at one wave crest, a second crest is at the middle of her boat, and a third is at the end.
What is the frequency of the waves? ____ Hz.
What is their wavelength? _____ m.
What is their speed? _____- m/s.
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.
To determine the frequency of the waves, we need to know how many complete wave cycles occur in one second. Given that the boat bobs up and down once every 2.0 seconds, the frequency can be calculated by taking the reciprocal of the time period:
Frequency = 1 / Time Period
Frequency = 1 / 2.0 s
Calculating this gives us the frequency of the waves.
To find the wavelength, we need to know the distance between consecutive wave crests. The problem states that when the front of the boat is at one wave crest, a second crest is at the middle of her boat, and a third crest is at the end. From this information, we can deduce that the distance between consecutive wave crests is equal to the length of the boat.
Wavelength = Length of the Boat
Wavelength = 3.0 m
Finally, to calculate the speed of the waves, we can use the formula:
Speed = Frequency * Wavelength
Substituting the previously calculated values:
Speed = Frequency * Wavelength
Speed = (1 / 2.0 s) * 3.0 m
Evaluating this expression gives us the speed of the waves.
By following these steps, we can arrive at the answers to the given questions.