While watching ocean waves at the dock of the bay, Otis notices that 13 waves pass beneath him in 32 seconds. He also notices that the crests of successive waves exactly coincide with the posts that are 7 meters apart. What are the period, frequency, wavelength, and speed of the ocean wave?
To find the period, frequency, wavelength, and speed of the ocean wave, we need to use the formulas related to wave motion.
1. Period (T): The period is the time it takes for one complete wave to pass a given point. It can be calculated using the formula:
T = Total time / Number of waves
In this case, the total time is 32 seconds and the number of waves is 13.
T = 32 s / 13 = 2.46 seconds
Therefore, the period of the ocean wave is 2.46 seconds.
2. Frequency (f): The frequency is the number of waves passing a point per unit time. It is the reciprocal of the period (f = 1/T). So the frequency can be calculated as:
f = 1 / T = 1 / 2.46 s ≈ 0.407 Hz
Therefore, the frequency of the ocean wave is approximately 0.407 Hz.
3. Wavelength (λ): The wavelength is the distance between two successive crests (or troughs) of a wave. In this case, the crests exactly coincide with the posts that are 7 meters apart. Therefore, the wavelength is 7 meters.
So, the wavelength of the ocean wave is 7 meters.
4. Speed (v): The speed of a wave can be calculated using the formula:
v = λ * f
where v is the speed, λ is the wavelength, and f is the frequency.
v = 7 m * 0.407 Hz ≈ 2.849 m/s
Therefore, the speed of the ocean wave is approximately 2.849 m/s.