A plucked guitar string makes 80 vibrations in one second. What is the period?
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A
0.0125 s
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B
0.025 s
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C
0.125 s
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D
0.25 s
A plucked guitar string vibrating 80 times per second has a period of 0.0125 seconds.
Period, defined as the time for one complete oscillation, is the reciprocal of frequency, and 1 divided by 80 Hz yields precisely 0.0125 s.
A) 0.0125 s
This correctly applies the relationship T=1/fâ. With 80 cycles per second, each cycle lasts 1/80=0.0125 seconds, a value typical for low-pitched musical notes and consistent with wave timing principles.
B) 0.025 s
This corresponds to a frequency of 40 Hz, half the given rate. It may result from halving the correct period or doubling the cycle count, but it does not reflect the stated 80 vibrations per second.
C) 0.125 s
This implies only 8 vibrations per second, which is an order of magnitude too low. Such a period would correspond to a sub-bass frequency far below that of a standard guitar string.
D) 0.25 s
This suggests a frequency of 4 Hz, which is infrasonic and not producible by a plucked guitar string. It grossly underestimates the oscillation rate and is physically implausible.
Conclusion
The period is the inverse of frequency, and 1/80 s equals 0.0125 s. The correct answer is A) 0.0125 s.
Topic Flashcards
Click to FlipWhat is the definition of the period of a wave or vibration?
The time it takes to complete one full cycle or oscillation.
What is the mathematical relationship between period (T) and frequency (f)?
T = 1 / f (Period is the reciprocal of frequency).
If an object vibrates at 80 Hz, what is its period? Show the calculation.
T = 1 / 80 Hz = 0.0125 seconds.
What is the standard SI unit for measuring period?
Seconds (s).
How would the period change if the guitar string made 160 vibrations per second instead of 80?
It would halve. T = 1/160 = 0.00625 s. Higher frequency means shorter period.