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Chapter 13: Problem 1

A bird flaps its wings 5 times a second. What are the frequency and period of this motion?

Short Answer

Expert verified
Frequency is 5 Hz, and the period is 0.2 seconds.

Step by step solution

01

Understanding Frequency

Frequency refers to how many cycles (or complete wave motions) occur per unit of time. In this scenario, the bird flaps its wings 5 times every second. Frequency is measured in hertz (Hz), which is equal to one cycle per second.
02

Calculating Frequency

The number of flaps per second is given as 5. Therefore, the frequency \( f \) of the bird flapping its wings is \( 5 \text{ Hz} \).
03

Understanding Period

The period is the time it takes to complete one cycle of motion. It is the inverse of the frequency. If a bird flaps its wings 5 times in one second, we can find the period (time for one flap) using the frequency.
04

Calculating Period

To find the period \( T \), use the formula \( T = \frac{1}{f} \), where \( f \) is the frequency. Substituting the frequency, we find \( T = \frac{1}{5} \text{ s} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Frequency
Frequency is a fundamental concept in harmonic motion and refers to the number of cycles or complete wave motions that occur in a unit of time. In simpler terms, how often something happens within a specific time frame. Frequency is typically measured in hertz (Hz), where one hertz equals one cycle per second. For example, if a bird flaps its wings 5 times each second, its frequency is 5 Hz. This means the bird's wing-flapping motion completes 5 full cycles every second. Understanding frequency helps us describe how rhythmic or rapid a motion is over time.
Period
The period of a wave or a motion is the time it takes to complete a single cycle. In harmonic motion, it provides insights into how long each cycle takes. Essentially, if frequency explains how often the cycles happen, the period explains the duration of each cycle. The relationship between period and frequency is inverse; as frequency increases, the period decreases and vice versa.

To calculate the period, you can use the formula:
  • Period, \( T = \frac{1}{f} \), where \( f \) is frequency.
For example, if a bird's wing flapping has a frequency of 5 Hz, the period \( T \) is calculated as \( T = \frac{1}{5} \) seconds. Hence, each flap takes 0.2 seconds. It鈥檚 a handy calculation when you want to know how long specific cycles last.
Cycles per Second
The term 'cycles per second' is another way of expressing frequency. It represents how many complete cycles, such as flaps or oscillations, occur in one second. This terminology may be less technical, but it's very descriptive and useful for understanding regular, repeating actions.
  • Equivalent to frequency in hertz (Hz): 1 cycle per second = 1 Hz.
Returning to our earlier example, when a bird flaps its wings 5 times in one second, it is completing 5 cycles per second. Thus, its frequency is said to be 5 Hz. The concept of cycles per second helps visualize the regularity of repeated motions and can simplify explanations and calculations of such patterns in various disciplines.

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