Frequency and Wavelength

Frequency and Wavelength - Definition and Examples

Introduction:


We all are familiar with the term wave. We have heard of water waves, sound waves and so on. So, what is a wave and what are its characteristics? What does a wave do? Are there different types of waves? What are the characteristic features, traits or defining aspects of what we call a wave? When you throw a stone in a lake of still water, we see ripples. Ripples are the wavy motion of the water which has a high point and a low point. These waves have distinct properties. These are similar to the more abstract waves like sound waves and light waves.

Many of us would have slinky, which is nothing but a coiled spring. When the long coil of spring is extended, the individual coils, assume a position of rest. Now when you repeatedly vibrate the first coil of the spring, this movement propagates along the entire length of the spring. 
 
For a wave to propagate, it requires a medium. Without a medium, a wave cannot travel. Just as a news media just carries the news without either creating it or by itself becoming the news, wave medium carries the wave. The medium by itself doesn't move. If you consider the medium as composed of a series of interacting particles, then the interaction of one particle with the other allows the disturbance to be passed on through the medium. In the case of the spring coil, the medium is the metal spring and in case of a sound wave, it is the air that is a medium.

Waves transport energy only and they do not transport matter. When there is a disturbance in a medium which causes a wave, the particles in the medium are temporarily displaced from their position. A restoring force brings them back to their original position in the media. In the case of the slinky wave, the first coil gets energy from the person who disturbs it, this first coil then transfers its energy to the second, but the first coil comes back to its original energy state. Thus, energy is transferred from one end to the other. When a duck sits on the water in a lake, which has ripples, will it be moved to the shore just by sitting there? If you said NO, then your answer is correct because the water doesn't move just the energy moves.

So, can we measure the size of a wave? How can we compare waves? How do we talk about waves? More importantly, can we measure the energy a wave carries? In order to do these, we need to understand the different types of waves, the different parameters of the waves and their relationship to each other.

Waves are categorized into 3 types based on the orientation of the particle relative to the direction in which energy is propagated along the wave.

  • 1. Longitudinal Wave: When the movement of the particles in the medium is parallel to the direction of movement of energy. When sound moves through the air, it follows this pattern.

  • 2. Transverse Wave: When the movement of particles in the medium is perpendicular to the direction of movement of energy. Ex: Wave through a rope.

  • 3. Surface waves: particles travel in a circular motion

  • Longitudinal waves can propagate through Liquids and gases, but transverse waves need a solid medium. Electromagnetic waves though can travel even through a vacuum. 

    There are some key terms to understand regarding waves before we go to frequency and wavelength.

    A crest is the highest point in a wave while a trough is the lowest point. Wave height is the vertical distance between the crest and its neighboring trough.

    Amplitude is half the wave height. It is the measure of the disturbance from the equilibrium position. The period is defined as the time taken by successive crests or trough to cross a particular point. The inverse of Period is frequency or in simple terms “how often does the medium or particles in medium vibrate”

    Frequency:


    A sound wave like any other wave is caused by a vibrating object. A tuning fork or a human voice. Regardless of the source that causes the vibration, the particles in the medium vibrate back and forth in a particular frequency. The term frequency indicates how often the particles vibrate when the wave passes through the medium. Frequency is measured as the total number of complete vibrations in unit time. For example, if a longitudinal wave undergoes 10000 vibrations in 5 seconds then its frequency is 2000 vibrations per second. The commonly used unit for frequency is Hertz. 

     1 Hertz = 1 vibration per second.

    What happens when you play guitar in a room? When a sound wave moves through a medium, each particle in that medium will vibrate at the same frequency. This is because each particle vibrates because of its nearest neighbor. Since only energy is transferred, they will vibrate at the same frequency as the previous one. So, when a guitar string vibrates at 500 Hz inside a room, the particles also vibrate at the same frequency and reach the ear and that is how we hear the sound. 
     
    The wave speed depends on the medium through which it travels. For example speed of light is lesser in a medium than when it travels through a vacuum. This will imply that the same frequency will correspond to a shorter wavelength in a medium than in a vacuum.


    The fluctuation in the air pressure caused by the sound waves can be detected by our ears and of course by other animals also. Humans can hear frequencies ranging between 20Hz and 20000HZ. Any sound of a frequency lower than the lowest frequency we can hear is called infrasound and anything more than the 20000 HZ is called ultrasound. The sensation caused by the frequency is called the pitch. When we say high pitch sound like a screech it's a high-frequency sound, similarly, a low pitch sound is a low-frequency sound.

    Wavelength:


    Now, what is Wavelength? Wavelength is defined as the distance between two consecutive crests or troughs in a wave. In a low-frequency wave, the distance between consecutive crests or trough is more than in a high-frequency wave. See the above figure for understanding. So, does this show a correlation between frequency and wavelength? A high-frequency wave has a lower wavelength. So, they are inversely related. Wavelength is measured in nanometres. Wavelength is indicated by the Greek symbol called Lambda. (λ). 

    The concept of wavelength is generally more commonly applied to waves of sinusoidal pattern. In a linear system, the sinusoid is the simplest forms with almost no disturbance to shape. 

    Light, sound, and water all travel as waves. The equation for their motion is the same and is given as
    F = c/λ

    Where F is the frequency of the wave, C is the speed of the wave and Lambda is the wavelength of the wave. In a given medium under fixed conditions, the speed of sound is constant. Suppose you are listening to a band playing with instruments of high and low frequency. If the speed of different frequencies were to be different, we would be hearing the high frequency first and then the low frequency, but that is not the case. They are all seeming to be in cadence. So, all frequencies must travel at almost the same speed. Since they travel at the same speed in a given medium, low-frequency sounds will have a higher wavelength, than high-frequency sounds. That is why the low-frequency sounds are generally coming out of the large speaker called Woofer and the small speaker called tweeter handles the high-frequency sounds. 

    Finally, we come to Electromagnetic waves. These can be described by their wavelengths, frequency and the energy they possess. These three parameters relate to different property of light, but they are all also related to each other. Light, as you may know, is an electromagnetic wave. However, the formula that links is the same as mentioned above for the other waves. All lights, regardless of color travel at the same speed, but their wavelengths being different causes different colors. It is this difference in wavelength that causes them to separate while passing through a prism. We can see this while doing the refraction through a prism experiment. In a spectrum, violet has the highest frequency with the lowest wavelength. At the other end is red. It has the lowest frequency and longest wavelength. So higher the energy of a wave, higher is the frequency and lower is the wavelength. So, colors of short wavelength and high frequency are more energetic than colors of longer wavelengths and lower frequency

    Thus, frequency and wavelength are two important parameters of a wave. When it comes to electromagnetic waves like light, these parameters also help determine the energy of the waves.