while watching ocean waves at the dock of the bay. otis notices that 10 waves pass beneath him in 30 seconds. he also notices that the crests of succesive waves exactly coincide with the posts that are 5 meters apart. what are the period frequency wavelength and speed of the ocean waves?
wavelength = 5 meters, given
period time/waves = 30 seconds/10 waves = 3 seconds
frequency = 1/period = 1/3 Hertz
speed = distance/time = 5/3 m/s
To find the period, frequency, wavelength, and speed of the ocean waves, we can use the following formulas:
1. Period (T) = time/number of waves
2. Frequency (f) = 1 / Period
3. Wavelength (λ) = distance between consecutive crests
4. Speed (v) = frequency * wavelength
Given Information:
Number of waves (n) = 10
Time (t) = 30 seconds
Distance between posts (d) = 5 meters
Step 1: Calculate the period (T)
Period (T) = t / n
Period (T) = 30 seconds / 10 waves
Period (T) = 3 seconds
Step 2: Calculate the frequency (f)
Frequency (f) = 1 / T
Frequency (f) = 1 / 3 seconds
Frequency (f) = 0.33 Hz
Step 3: Calculate the wavelength (λ)
Wavelength (λ) = Distance between posts (d)
Wavelength (λ) = 5 meters
Step 4: Calculate the speed (v)
Speed (v) = Frequency (f) * Wavelength (λ)
Speed (v) = 0.33 Hz * 5 meters
Speed (v) = 1.65 m/s
Therefore, the period of the ocean waves is 3 seconds, the frequency is 0.33 Hz, the wavelength is 5 meters, and the speed is 1.65 m/s.
To find the period, frequency, wavelength, and speed of the ocean waves, we'll use the given information.
1. Period (T): The period is the time it takes for one complete wave to pass a given point. In this case, we know that 10 waves pass beneath Otis in 30 seconds. Thus, we can calculate the period by dividing the total time (30 seconds) by the number of waves (10).
T = Total time / Number of waves
T = 30 seconds / 10 waves
T = 3 seconds
Therefore, the period of the ocean waves is 3 seconds.
2. Frequency (f): The frequency is the number of waves passing a given point per unit of time. It is the reciprocal of the period.
f = 1 / T
f = 1 / 3
f ≈ 0.33 Hz
Therefore, the frequency of the ocean waves is approximately 0.33 Hz.
3. Wavelength (λ): The wavelength is the distance between any two successive identical points on a wave, such as crest to crest or trough to trough. In this scenario, we know that the crests of successive waves coincide with the posts that are 5 meters apart. Therefore, the wavelength is equal to the distance between the posts.
λ = Distance between the posts
λ = 5 meters
Therefore, the wavelength of the ocean waves is 5 meters.
4. Speed (v): The speed of a wave is calculated by multiplying the wavelength by the frequency.
v = λ * f
v = 5 meters * 0.33 Hz
v ≈ 1.65 m/s
Therefore, the speed of the ocean waves is approximately 1.65 m/s.
To summarize:
- Period (T) = 3 seconds
- Frequency (f) ≈ 0.33 Hz
- Wavelength (λ) = 5 meters
- Speed (v) ≈ 1.65 m/s