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Chapter 6: Problem 2

A periodic wave has a frequency of \(5.0 \mathrm{Hz}\). What is the wave period?

Short Answer

Expert verified
The wave period is 0.2 seconds.

Step by step solution

01

Identify Known Variables

We know from the problem statement that the frequency of the wave is given as \( f = 5.0 \text{ Hz} \).
02

Recall Relationship Between Frequency and Period

The period \( T \) of a wave is the reciprocal of its frequency \( f \). The relationship is given by the formula \( T = \frac{1}{f} \).
03

Substitute the Frequency Into the Formula

Using the formula \( T = \frac{1}{f} \) and substituting \( f = 5.0 \text{ Hz} \), we find that \( T = \frac{1}{5.0} \).
04

Calculate the Wave Period

Perform the division to calculate the period: \( T = 0.2 \text{ seconds} \).

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Key Concepts

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

Understanding Frequency
Frequency is an important concept when it comes to understanding waves, whether in physics or in our everyday lives. It tells us how often something repeats itself over a certain period of time. For waves, frequency specifically refers to how many wave cycles occur in one second.
In the context of the exercise, the wave's frequency is given as 5.0 Hz. This means that there are five complete cycles of the wave every second.
  • The higher the frequency, the more cycles that occur per second.
  • Frequency is measured in hertz (Hz), where 1 Hz equals one cycle per second.
Frequency is a fundamental property that helps define the behavior and characteristics of various types of waves, including sound waves, light waves, and water waves.
Exploring the Reciprocal Relationship
In wave mechanics, the reciprocal relationship between frequency and period is a key principle. Simply put, the frequency (\(f\)) and the period (\(T\)) of a wave are inversely related.
When you increase frequency, the period decreases, and vice versa.
The reciprocal relationship can be understood with the formula:
  • \( T = \frac{1}{f} \)
Here's how it works: if a wave has a high frequency, its cycles are more frequent and shorter, resulting in a smaller period. Conversely, a low frequency wave with fewer cycles per second will have a longer period. Remember, this relationship helps us calculate one value if we are given the other. It's a fundamental aspect of understanding how waves operate.
How to Perform Period Calculation
Once the relationship between frequency and period is understood, calculating the period when the frequency is known becomes straightforward.
In the exercise above, we know the wave's frequency is 5.0 Hz. With the reciprocal relationship formula, \( T = \frac{1}{f} \), calculating the period becomes a simple substitution task.
  • First, substitute the frequency value into the formula: \( T = \frac{1}{5.0\, \text{Hz}} \).
  • Then, perform the calculation: \( T = 0.2 \text{ seconds} \).
This means that each cycle of the wave takes 0.2 seconds. Period calculation thus provides a complete picture of one wave cycle's duration. Understanding how to perform this calculation helps solidify the reciprocal relationship, making it easier to convert between frequency and period as needed in various scientific contexts.

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Most popular questions from this chapter

Compute the wavelength in air of ultrasound with a frequency of \(50 \mathrm{kHz}\) if the speed of sound is 344 \(\mathrm{m} / \mathrm{s}\).

A sound wave has a frequency of \(3000 \mathrm{Hz}\). What is the distance between crests or compressions of the wave? (Take the speed of sound to be \(344 \mathrm{m} / \mathrm{s}\)) .

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A sound wave in a solid has a frequency of \(15.0 \mathrm{kHz}\) and a wavelength of \(0.333 \mathrm{m}\). What would be the wave speed, and how much faster is this speed than the speed of sound in air?
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