Extract:
A hummingbird’s wings beat at 25 beats per second. What is the period of the wing beating in seconds?
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A
0.04 s
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B
0.25 s
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C
0.4 s
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D
4 s
The period of the wing beating is 0.04 seconds.
Frequency and period are reciprocals of each other. Frequency measures how many cycles occur per second, in hertz, while the period measures the time taken for one complete cycle. With a wing-beat frequency of 25 beats per second, the time for a single beat is found by taking the reciprocal of the frequency.
A) 0.04 s
The period is calculated using the relationship:
period equals one divided by frequency
Substituting the given frequency gives:
period equals one divided by 25 per second
period equals 0.04 seconds
This correctly represents the time for one wing beat.
B) 0.25 s
A period of 0.25 seconds would correspond to a frequency of 4 beats per second. This option confuses the given frequency with a quarter of a second rather than taking the reciprocal.
C) 0.4 s
A period of 0.4 seconds would imply a frequency of 2.5 beats per second. This results from a decimal placement error when inverting the frequency.
D) 4 s
A 4-second period corresponds to a frequency of 0.25 beats per second, which is far slower than the given wing-beat rate. This reflects reversing the numerator and denominator incorrectly.
Conclusion
The period of motion is found by taking the reciprocal of the frequency. For a hummingbird wing-beat rate of 25 beats per second, the period is 0.04 seconds.
Topic Flashcards
Click to FlipDefine the terms period (T) and frequency (f) in physics. What is their mathematical relationship?
Frequency (f) is the number of cycles (or beats) per second, measured in Hertz (Hz). Period (T) is the time for one complete cycle, measured in seconds (s). Their relationship is: T = 1/f and f = 1/T.
Using the formula T = 1/f, calculate the period of a pendulum that swings with a frequency of 2 Hz.
T = 1 / f = 1 / 2 Hz = 0.5 seconds.
A hummingbird's wings beat 25 times per second. Express this frequency in the proper SI unit (Hertz) and then find the period.
Frequency, f = 25 Hz. Period, T = 1 / 25 Hz = 0.04 s.
If the period of a sound wave is 0.002 seconds, what is its frequency in Hertz?
f = 1 / T = 1 / 0.002 s = 500 Hz.
What would happen to the period if the hummingbird's wing-beat frequency doubled to 50 beats per second?
The period would be halved. T = 1 / 50 Hz = 0.02 s. This demonstrates the inverse relationship: doubling frequency halves the period.