Select the correct answer.
Honey bees beat their wings, making a buzzing sound at a frequency of 2.3 x 102 hertz. What is the period of a bee's wing beat?
A. 4.3 x 103 seconds
B. 2.6 x 103 seconds
C. 4.0 x 103 seconds
D. 2.6 x 103 seconds
Answer (2)
The problem gives the frequency of a bee's wing beat as 2.3 × 1 0 2 hertz.
Recall the formula relating period T and frequency f : T = f 1 .
Substitute the given frequency into the formula: T = 2.3 × 1 0 2 1 = 4.3 × 1 0 − 3 seconds.
The period of the bee's wing beat is 4.3 × 1 0 − 3 seconds .
Explanation
Understanding the Problem The problem provides the frequency of a honey bee's wing beat and asks for the period. We know that frequency and period are inversely related.
Recalling the Formula The relationship between frequency f and period T is given by the formula: T = f 1 where T is the period in seconds and f is the frequency in hertz.
Substituting the Given Value We are given that the frequency f = 2.3 × 1 0 2 hertz. Substituting this value into the formula, we get: T = 2.3 × 1 0 2 1
Calculating the Period Calculating the period: T = 230 1 ≈ 0.0043478
Expressing in Scientific Notation Expressing the result in scientific notation: T ≈ 4.3 × 1 0 − 3 seconds
Selecting the Correct Answer Comparing the calculated period with the given options, we find that option OA, 4.3 × 1 0 − 3 seconds, matches our calculated value.
Examples
Understanding the period of oscillating systems is crucial in various fields. For instance, in music, the frequency of a sound wave determines the pitch we hear, and the period is the duration of one cycle of the wave. Similarly, in electrical engineering, the frequency of an alternating current (AC) determines how many times the current changes direction per second, and the period is the time it takes for one complete cycle. Knowing the relationship between frequency and period helps engineers design circuits and musicians tune instruments.
To find the period of a bee's wing beat, we use the relationship T = f 1 where f = 2.3 × 1 0 2 Hz . This results in a period of approximately 4.3 × 1 0 − 3 seconds . Based on the provided options, the correct period does not seem to match, indicating an error in the choices presented.
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