In one minute, 15 waves break onto the shore. What is the frequency of the waves?
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A
0.15 Hz
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B
0.2 Hz
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C
0.25 Hz
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D
0.4 Hz
The frequency of the waves is 0.25 Hz.
With 15 complete wave cycles occurring over a 60-second interval, the number of cycles per second, the definition of frequency, is exactly one-quarter of a hertz.
A) 0.15 Hz
This would correspond to only 9 waves per minute, not the 15 observed. It likely results from an incorrect conversion, such as dividing by 100 instead of 60, and does not match the given wave count.
B) 0.2 Hz
This implies 12 waves per minute (0.2 × 60), which is fewer than the stated 15. It underestimates the actual frequency and misrepresents the timing of the wave arrivals.
C) 0.25 Hz
This is correct, as frequency is calculated by dividing the number of waves by the time in seconds: f=15/60=0.25 Hz. This means one wave arrives every 4 seconds, which aligns with typical ocean wave behavior.
D) 0.4 Hz
This suggests 24 waves per minute, exceeding the given data. It may stem from confusing frequency with period (e.g., calculating 60 ÷ 15 = 4 s and then misinterpreting it as 0.4 Hz), which is a fundamental error in wave analysis.
Conclusion
Frequency must be expressed in cycles per second, and only 0.25 Hz matches the observation of 15 waves in 60 seconds. The correct answer is C) 0.25 Hz.
Topic Flashcards
Click to FlipIf 24 waves pass a fixed point in 2 minutes, what is the frequency of the waves in hertz (Hz)?
0.2 Hz. (Frequency = number of waves / time in seconds = 24 / 120 = 0.2 Hz).
A wave generator produces waves with a period of 5 seconds. What is the frequency of these waves?
0.2 Hz. (Frequency = 1 / Period = 1 / 5 s = 0.2 Hz).
The frequency of a water wave is 0.5 Hz. How many waves will arrive at the shore in 30 seconds?
15 waves. (Number of waves = frequency × time = 0.5 Hz × 30 s = 15).
What is the period (in seconds) of a wave with a frequency of 0.25 Hz?
4 seconds. (Period = 1 / frequency = 1 / 0.25 Hz = 4 s).
If the frequency of a wave is tripled, what happens to its period?
The period becomes one-third of the original value. (Period is inversely proportional to frequency).