A woman is standing in the ocean, and she notices that after a wave crest passes by, five more crests pass in a time of 68.0 s. The distance between two successive crests is 34.1 m. What is the wave's (a) period, (b) frequency, (c) wavelength, and (d) speed?
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To find the answers to these questions, we can use the formulas related to waves. Let's break it down step by step:
(a) To find the wave's period, we need to know the time it takes for one wave crest to pass. In this case, we know that after a wave crest passes, five more crests pass in a time of 68.0 seconds. This means that the time for six wave crests to pass is 68.0 seconds. To find the period, we divide the total time by the number of wave crests:
Period = Total time / Number of wave crests
Period = 68.0 s / 6
Period = 11.3 s
Therefore, the wave's period is 11.3 seconds.
(b) The frequency of a wave is the number of wave crests passing a given point per second. To find the frequency, we take the inverse of the period:
Frequency = 1 / Period
Frequency = 1 / 11.3 s
Frequency ≈ 0.0885 Hz
Therefore, the wave's frequency is approximately 0.0885 Hz.
(c) The wavelength of a wave is the distance between two successive wave crests. In this case, we are given that the distance between two successive crests is 34.1 meters.
Therefore, the wave's wavelength is 34.1 meters.
(d) The speed of a wave is given by the equation:
Speed = Wavelength * Frequency
Substituting the known values, we get:
Speed = 34.1 m * 0.0885 Hz
Speed ≈ 3.02 m/s
Therefore, the wave's speed is approximately 3.02 m/s.
To summarize:
(a) The wave's period is 11.3 seconds.
(b) The wave's frequency is approximately 0.0885 Hz.
(c) The wave's wavelength is 34.1 meters.
(d) The wave's speed is approximately 3.02 m/s.