[Physics Class Notes] on Frequency and Wavelength Pdf for Exam

We have heard of waves in our everyday lives like water waves and sound waves. On this page, we will learn what a Wave is and its primary characteristics.

We can define a Wave as a continuous and recurring disturbance of a medium.

In our world, we observe various phenomena like throwing a stone in the water and seeing ripples, plucking the strings of a guitar, an oscillating string of thread, earthquake waves, and tsunami waves.

A wave needs a medium to propagate. Without this medium, a wave would not be able to travel. The medium itself does not move, but if we look at it as an interlinked series of several particles, we can say that when a wave interacts with one particle. It allows the wave to pass through the disturbance to the interacting particles. For example, a spring coil has a medium of a metal spring, just like in the case of a sound wave, the air through which that wave travels is its medium

Waves only transport energy and do not matter. Suppose there is a disturbance in the medium which is transporting the wave. In that case, the particles temporarily become displaced from their position and only get back to their original position if a restoring force brings them back there.

Types of Waves

We can categorize waves into three types. This depends on how the particles are directed and propagated through that wave:

Transverse Wave: When the particle movement is perpendicular to the energy’s direction of the movement in the medium. Example: Wave of a rope.

Longitudinal Wave: When the particle movement is parallel to the energy’s direction of the movement in the medium. Example: Sound moving through the air and forming a pattern.

Surface Waves: When the particle movement occurs along the energy’s direction of the movement in the medium in a circular motion. Example: Seismic Waves, Electromagnetic Waves

Before getting into Frequency and Wavelength, let us know some more essential terms.

Crest: A crest is the highest point of the wave.

Trough: The trough is the lowest point in a wave.

Wave Height: Wave Height is the vertical distance we can observe between the crest and the trough near it.

Amplitude: An amplitude is half of the height of a wave. We can define amplitude as the measure of disturbance in a substance from the equilibrium position.

Frequency

The term frequency means the number of times a particle vibrates when the sound wave passes through a medium. We measure frequency as the total number of vibrations in a unit of time. 

For example, suppose a longitude wave vibrates about 10000 vibrations in 5 seconds. In that case, its frequency will be 2000 vibrations per second. The unit for frequency is Hertz.

1 Hertz = 1 Vibration/Second

When a sound wave travels through a medium, each particle in that medium vibrates at the same frequency. This happens because each particle vibrates due to its neighboring particle. Since only energy gets transferred, they vibrate at the same frequency as the previous particles.

The speed of a wave also depends on the medium through which it travels. For example, the speed of light is lesser in a medium when it travels through a vacuum instead of air. This also tells us that this same frequency corresponds to a shorter wavelength in any medium than the vacuum.

Wavelength

Wavelength can be defined as the distance between the two consecutive crests or troughs in a curve. In a high-frequency wave, the distance between the crests and troughs is less than in a low-frequency wave and vice-versa.

Frequency is inversely related to Wavelength.

We measure Wavelength in nanometers, denoting it by the Greek Symbol Lambda (λ).

We more commonly apply the concept of a wavelength to waves of a sinusoidal pattern.

Sinusoidal Pattern is also commonly known as a Sine Wave, which describes a smooth periodic oscillation. A Sine wave is continuous, and we name it after the sine function.

In a linear system, we observe that the sinusoid is one of the simplest forms without disturbing its shape.

Mediums like Light, Water, and Sound all travel as waves. The equation we use to donate their motion is the same, which is:

F = c/λ

Here, we see that F is the wave’s frequency, whereas c is the speed, and Lambda is the Wavelength.

We can find Electromagnetic Waves in mediums like Light. We can describe them by their frequency, wavelengths, and energy. These three properties of the electromagnetic wave relate to Light and one another. 

All lights travel at the same speed regardless of their color. However, if their wavelengths are different, they can turn into different colors. We can often see these lights separate into different colors in a prism. Red has the lowest frequency and the longest Wavelength in that spectrum that we produce. In contrast, on the other end, violet has the highest frequency but the lowest Wavelength.

This tells us that the higher the wave’s energy, the higher is the frequency and the longest Wavelength. In the same way, colors of a short wavelength also have a high frequency. They are more vibrant than the colors with a longer wavelength and lower frequency.