While watching ocean waves at the dock of the bay, Otis notices that 13 waves pass beneath him in 26 seconds. He also notices that the crests of successive waves exactly coincide with the posts that are 5 meters apart. What are the period, frequency, wavelength, and speed of the ocean wave?
What do you think? It's pretty easy to figure out from the information provided.
Remember that wave speed equals frequency time wavelength.
Period (in seconds) = 1/Frequency (in Hz)
To find the period, frequency, wavelength, and speed of the ocean wave, we can use the following formulas:
Period (T) = time taken for one complete wave cycle
Frequency (f) = number of complete wave cycles per second
Wavelength (λ) = distance between two successive crests or troughs
Speed (v) = distance traveled by a wave per unit time
Given:
Number of waves passing in 26 seconds (n) = 13
Distance between posts (d) = 5 meters
To find the period:
The period is the time taken for one complete wave cycle. Since there are 13 waves passing in 26 seconds, the period can be calculated as follows:
T = time / number of waves
T = 26 seconds / 13
T = 2 seconds
So, the period (T) of the ocean wave is 2 seconds.
To find the frequency:
Frequency is the number of complete wave cycles per second. Since the period is 2 seconds, the frequency can be calculated as:
f = 1 / T
f = 1 / 2
f = 0.5 Hz
So, the frequency (f) of the ocean wave is 0.5 Hz.
To find the wavelength:
The wavelength is the distance between two successive crests or troughs. In this case, the distance between two posts is given as 5 meters, which corresponds to one wavelength. Therefore:
λ = distance between posts
λ = 5 meters
So, the wavelength (λ) of the ocean wave is 5 meters.
To find the speed:
The speed of a wave is the distance traveled by the wave per unit time. The speed can be calculated as the product of the frequency and the wavelength:
v = f * λ
v = 0.5 Hz * 5 meters
v = 2.5 m/s
So, the speed (v) of the ocean wave is 2.5 m/s.