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Question

while watching ocean waves at the dock of the bay, Otis notices that 10 waves pass beneath him in 30sec. he also notice that the crests of successive waves exactly coinade with the past that are 5meters apart. What are the peroid,frequency,wavelength, and speed of the ocean wave.

Answer 1

Period: The time for one full wave to pass.
You get 10 in 30 seconds,
so 30 sec/10 waves = 3 seconds per wave

Frequency: The number of cycles per second is the number of Hertz (Hz)
You get 10 crests in 30 seconds,
so 10 cycles/30 seconds = .33 Hz

Wavelength: The distance between crests.
5 meters

Speed: Distance per unit time
One wave passes in 3 sec (period) and the wavelength (5 m) is how far it went in the period.
so, 5 meters/ 3 sec = 1.66 m/s

Answer 2

The wavelength is the length for one complete wave cycle, which as the problem states is 5m.

Since 10 waves pass in 30 seconds, and we know each wave has the length of 5m, we can say that 50m pass every 30 seconds, and thus the speed is 50m per 30 seconds, or 1.667 m/s.

The frequency is defined as waves or cycles per second. We know that 10 waves pass every 30 seconds, which means every second 1/3 of a wave will pass. The unit of waves per second is also known as Hz (Hertz), thus 0.3333 Hz.

The period is the inverse of frequency, or the time for one wave to complete its cycle. We can inverse 0.3333 Hz to see that the answer is 3 s (seconds), or we can also see that from 10 waves per 30 seconds, that means that every 3 seconds, 1 wave will pass.