For a Given Wave, if the Frequency Doubles, the Wavelength

Introduction:

In the field of physics, waves are a fundamental concept that play a key role in understanding the behavior of various phenomena. Waves can be characterized by their frequency and wavelength, both of which influence their properties. In this article, we will explore the relationship between the frequency and wavelength of a wave, specifically focusing on what happens to the wavelength when the frequency doubles.

I. The Basics of Waves:

Before delving into the relationship between frequency and wavelength, it is essential to understand the basic properties of waves. A wave is a disturbance that travels through a medium, transferring energy without displacing matter permanently. Waves can be classified into different types, such as mechanical waves, electromagnetic waves, and transverse waves. Throughout this article, we will refer to a generic wave.

II. Understanding Frequency and Wavelength:

Frequency and wavelength are two fundamental characteristics of a wave. Frequency refers to the number of complete oscillations or cycles that a wave undergoes per unit of time. It is typically measured in hertz (Hz), where one hertz represents one cycle per second. On the other hand, the wavelength represents the distance between two consecutive points of similar phase on a wave. It is usually denoted by the symbol lambda (λ) and is measured in meters (m).

III. The Relationship between Frequency and Wavelength:

According to the wave equation, the equation that describes the relationship between frequency, wavelength, and the speed of the wave, we have:

v = f * λ

where v represents the speed of the wave, f is the frequency, and λ denotes the wavelength. This equation illustrates that the product of frequency and wavelength is equal to the speed of the wave.

IV. Doubling the Frequency:

Now, let’s examine what happens when the frequency of a wave doubles. If we consider the wave equation, we can rearrange it to solve for the wavelength:

λ = v / f

As the frequency doubles, we can substitute the new value into the equation:

λ = v / (2f)

From this equation, we can see that when the frequency doubles, the wavelength is halved. In other words, the wavelength becomes half of its original value when the frequency doubles.

V. Examples:

To better understand this relationship, let’s consider a practical example. Suppose we have a wave traveling at a speed of 10 m/s with an initial frequency of 5 Hz. Using the equation, we can calculate the wavelength:

λ = 10 m/s / 5 Hz

λ = 2 m

Now, if we double the frequency to 10 Hz while keeping the speed constant, we can calculate the new wavelength:

λ = 10 m/s / (2 * 10 Hz)

λ = 0.5 m

As expected, the wavelength has halved from its original value.

Conclusion:

In conclusion, the relationship between frequency and wavelength in a wave is inversely proportional. When the frequency doubles, the wavelength is halved. This principle holds true for various types of waves and plays a crucial role in understanding the behavior and properties of waves. Knowing this relationship allows scientists and researchers to make predictions and calculations involving wave phenomena accurately.