Unit of Wavelength

By definition, the wavelength is the distance between two consecutive crests and troughs. In simple words, the distance between two subsequent peaks in a wave is known as wavelength. To better understand the concept of wavelength, let’s take a deep dive into what waves are. 

What are Waves? 

Waves are disturbances that travel from one location to another in a medium. When waves are propagating from one point to another, the medium remains stationary for the larger part and moves locally.

A perfect example of a wave would be a telephone coil. When you take a telephone coil and stretch it slightly, you’d get a squiggly shape with even spaces between each upward and downward curve. Holding the coil at this position would be known as the rest position or equilibrium. Now if you move the coil from one end in any direction, the entire coil would go through a disturbance before coming back to the rest position. 

The act of creating a disturbance in the coil before it comes back to the rest position would be known as ‘pulse’. However, if you make the same disturbance repeatedly, it would result in the coil moving continuously and periodically in a back and forth manner. The repeated and periodic disturbance that moves through a medium for a prolonged period of time from one location to another is known as a wave. 

What is a Medium? 

We talked about the concept of a medium in the previous paragraph but what does it actually mean? A medium is a substance or material which carries a wave. The medium doesn’t make or produce a wave, but simply transports or carries it from one point to another. For example, in the telephone coil, the wave was not produced by the coil itself, however, it was able to travel from one end to another due to the particles in the coil. The particle to particle interaction in a medium is what results in the propagation of the waves. 

To understand the nature of a wave, it is important to consider the medium as a collection of interacting particles. To visualize this concept, imagine a house of cards, now the cards are the medium. If you push even one of the cards in the house, the ones adjacent to it will also feel the force applied and therefore move away. This disturbance would result in a wave, where every particle (card) would interact with one another to carry the wave to the entirety of the medium (house of cards).

About Waves, Transmit Energy

One of the unique properties of waves lies in the fact that waves transmit energy without transporting matter. When a disturbance is caused in the medium, the waves carry over the energy from one particle to another without transporting or disturbing the matter at all. For eg; when someone pushes a ball down a hill, the energy is transported from the top of the hill to the ground, however, this action is possible only when the ball rolls down the hill too. However, in a wave, for eg, in a telephone coil, the energy is displaced from one particle to the coil to the other till it reaches the end of the coil, but the matter (or particles of the coil) remain stationary as once the energy has been displaced from one crest to the other, the previous particle reverts back to its rest position (state of equilibrium). 

How was the Wavelength Discovered?

The waves were discovered in the 1800s by Sir William Herschel when he was exploring the question of how much heat was contained by the different colors of visible light. He conducted an experiment, where he used a glass prism to break down white light into its composing colors. After this, he placed a thermometer under each color and placed another thermometer just beyond the range of red light, which is the last color in the VIBGYOR spectrum. Through this experiment, he discovered that the thermometer that was placed beyond the range of white light has the highest temperature. And this was the story of how infrared waves were discovered. Based on this discovery, many scientists went forward and discovered many other components and types of waves. 

Components of a Wave

A wave consists of the following components: 

• Rest position: the undisturbed position of the particle is known as the rest position. In a diagram or graph, the x-axis of the graph is known as the rest position. 

• Displacement: the entire length of the wave from one end to another is known as displacement. 

• Crest: the highest point of the peak from the rest position is called a crest. 

• Trough: the lowest point of the peak from the rest position is called a through.

• Amplitude: the distance between the crest or trough from the rest position is known as amplitude. 

• Wavelength: the distance between two consecutive crests or troughs is called a wavelength. It is denoted by the Greek symbol lambda ƛ. The standard unit of wavelength is metered (m). 

• Time period: The time taken for a wave to complete one whole cycle of a crest and trough is known as the time period. The SI unit of the time period in seconds (s). 

• Frequency: the number of waves that pass through a point per second derives from the frequency of the wave. Frequency is measured in Hertz (Hz). 

How is Wavelength Calculated?

The wavelength of a wave is calculated by dividing the velocity of a wave by its frequency. 

wavelength= wave velocity/ frequency

ƛ = v/f

Here, ƛ = distance between the two consecutive crests or troughs in meters. 

           V = velocity of the speed of waves moving in a direction, calculated in m/s.

           f = frequency of the wave in Hz or per second. 

Types of Waves

Waves come in many shapes and forms and usually have the same characteristics to a certain degree. However, based on some distinguishing factors, we can categorize waves into two different categories. 

Basis of the Direction of Movement

Categorizing waves on movements results in three different categories: 

• Transverse Waves: transverse waves are the waves in which the particles of the medium move perpendicular to the direction in which the wave moves. For eg, in a telephone coil, when the disturbance is induced at one end, the wave moves from left to right. However, the particles of the coil oscillate in up and down motion. This results in a formation of a transverse wave. 

• Longitudinal Wave: Longitudinal waves are the waves in which the particles of the medium move parallel to the direction of the wave. A sound wave is a classic example of this type of wave. When a sound wave is produced, the sound wave moves from the lips of the speaker to the ears of the listener. While the air molecules that carry the sound wave vibrate back and forth in the same direction of the wave. When one strikes a tuning fork against a hard surface, the pitches of the tuning fork move back and forth rather than up and down. 

• Surface Wave: A surface wave is a wave in which the particles of the medium undergo a circular motion. These types of waves are considered either transverse or longitudinal. For example, the waves on the surface of the ocean do not move back or forth or up and down, instead, they fold over and move in a circular motion. 

Basis of Medium 

This categorization rests on the principle that a wave can transmit energy in a vacuum or not. This type of categorization leads to two types of waves: 

• Electromagnetic Waves: an electromagnetic wave is a wave that is capable of transporting energy through a vacuum. These waves are produced from the energy of charged particles. The sun rays are the best example of this type of wave since sun rays can easily transmit energy even without a medium. 

• Mechanical Waves: waves that require a medium to transport energy and are incapable of existing in a vacuum. A sound wave is an example of a mechanical wave since sound waves can only be produced through the oscillation of air molecules. This is the reason why one can’t hear anything in space. 

Brief of Light Waves

Visible light is the range of light in the electromagnetic spectrum that can be seen by the human eye. The electromagnetic spectrum consists of all the electromagnetic radiations that exist in our environment. This includes gamma rays, x-rays, ultraviolet rays, infrared light, visible light, radio waves, and microwaves. The visible spectrum for humans ranges from the wavelength of 380-740 nm. A nanometer is a billionth fraction of a meter, which means that there is a very small window of the electromagnetic spectrum that is visible to the human eye. Since our planet is rich and abundant in diversity with various species with different anatomies, there are animals who can see various other portions of the electromagnetic spectrum. For example, Honeybees can see light in the ultraviolet spectrum, while snakes can see infrared light. 

In humans, the wavelengths of visible light are associated with colour perception, while the amplitude of a wave is associated with the brightness of the light. The larger the amplitude of a wave, the brighter it would appear to the human eye. In a rainbow, when white light is refracted in seven different colours, the light with longer wavelengths is perceived as red by the human eyes, the intermediate wavelengths appear to be green, while the light with the shortest wavelengths is seen in the shades of blue. 

White light = Violet, Indigo, Blue, Green, Yellow, Orange, Red (mentioned in the order of shortest to longest wavelengths).

Brief of Sound Waves

Just like light waves, the various components of a wave are associated with the human perception of sound. The pitch of a sound wave is determined by its frequency. High-frequency sound waves sound shrill or high-pitched to the human ear, while the low-frequency sound waves appear to be low-pitched or deep in nature. The audible range of sound frequencies for humans ranges from 20 - 20,000 Hz. Most humans show heightened sensitivity to sound waves that fall in the middle of this range. 

As you may have noticed, the training whistle used for dogs can’t be heard by humans at all, however, it alerts the dogs at one go. How is that possible? That is possible because dogs can hear the sound waves from the range of 70-45,000 Hz. Due to a higher range of frequencies exhibited by them, dogs are much more sensitive to sound than humans. 

Apart from this, cats also show excellent sensitivity to sound waves due to their broad range of frequencies. They can hear sound waves in the range of 55 Hz - 79,000 Hz, which is even broader than dogs. 

The loudness of a sound is based on the amplitude of the sound wave. The higher the amplitude of a sound wave, the louder the sound would be. The loudness of a sound wave is measured in decibels (db), which is the unit of measurement of the intensity of sound waves. A typical conversation happens at around 60 db. However, sound waves ranging from 80-130 db can be fatal and cause hearing damage. 

Even though amplitude is associated with the loudness of the sound, there are certain interactions between the frequencies and amplitudes that result in unique phenomena. For example, a 10 Hz sound wave will be inaudible to the human ear, despite a larger amplitude. Similarly, a 1000 Hz sound wave might be audible to the human ear even when it has a very low amplitude. 

Practical Examples of Waves in our Everyday Life

• X-rays: X-rays are well known for revealing the bone structure of a human body by permeating through the skin surface. From spotting fractures to killing cancer cells. X-rays have various applications in real life. X-rays are an example of transverse waves. Most X-rays have a wavelength ranging from 10 nanometers to 10 picometers, which allows them to visualize much smaller structures as compared to what can be seen under a conventional optical microscope. 

• Radio Waves: Radio waves are an example of transverse waves and exist as a series of repeated crests and troughs. These waves have the longest wavelengths in the electromagnetic spectrum ranging from 1 millimeter to over 100 kilometers. These types of waves are extensively used in radio transmissions, air-traffic control, remote-control toys, artificial satellites, etc. 

• Microwave: Microwaves are a type of electromagnetic radiation which have a wide range of applications. They are used in microwave ovens to cook food, in radars and communication devices, etc. Microwaves have a wavelength that ranges from 1 millimeter to 1 meter. 

• Acoustic Microscopy: Acoustic microscopy involves the use of longitudinal waves to penetrate solid objects to reveal their internal features such as cracks, voids, and fissures. This type of technology uses very high-frequency ultrasound waves which usually have a wavelength of 1.9 centimeters or less. 

• Sonography: Sonography uses ultrasound waves to create images of internal body parts such as tissues, muscles, joints, and internal organs. The sonograms, also known as ultrasound images, are formed by transferring ultrasound waves into tissues using a probe, which results in a real-time image formation. 

Wave Equation

The wave equation is the mathematical expression between the speed, wavelength, and period of time. A wave is generated when a disturbance is caused to a particle in a medium. This leads to the creation of a wave pattern that moves from particle to particle in a medium. The frequency of each particle is equal to the frequency of vibration of the source particle ( the first particle where the disturbance was caused). Likewise, the period of vibration of every particle is equal to the period of vibration of the source particle. In one period, the source particle moves in a wavy motion: from the rest position to upwards, back to the rest position, from the rest position to downwards, and then back to the rest position. This back and forth movement leads to the completion of one wave cycle. 

Therefore, we can say that by the time one period has elapsed, the wave travels the distance of one wavelength. Now combining this information with the pre-existing knowledge of the equation of speed, which is speed = distance/time, we can derive the speed of the wave, which is 

Speed = wavelength / Period…………….(1)

As already mentioned above, the frequency is calculated in the units per second. This means period is the reciprocal of the frequency. Therefore, 1 time period would equal 1/f. 

Substituting the values of the period in the equation (1) with this information, we get the new equation, 

Speed = wavelength x frequency 

This above-mentioned equation is known as the wave equation. A wave equation is the mathematical expression of the relationship between speed, wavelength, and frequency and is used to analyze the motion of the waves. 

Wavelength and its Unit

Wavelength is the length of a wave from the highest point of a crest to the highest point of the adjacent crest or the lowest point of a trough to the lowest point of an adjacent trough. It is denoted by a symbol called Lambda (λ). As per the given definition, we know that wavelength is the length thus the S.I unit of wavelength should be the same as the S.I unit of length. We know, the S.I unit of length is a meter so the SI unit of wavelength is also a meter.

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Definitions of Metre:

Meter Can be Defined in Different Ways:

• In terms of prototype meter bar: To maintain the new metric standard of length ‘The International Bureau of Weights and Measures’ constructed and preserved a prototype meter bar. This bar is made up of alloy (90% platinum and 10% iridium). One meter is the distance measured between two lines on this bar at zero degrees. In other words, the length of this bar is taken as 1 meter.

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• In terms of the Distance between Latitudes: Meter is one ten-millionth of the maximum distance between the Equator and the North pole. The distance between the equator and the North pole is 10,000 km. The unit Kilometre is derived from the meter. Kilo means 1000 times thus 1 kilometer is equal to 1000 meters.

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• In terms of Light: One meter is the distance traveled by light in a vacuum in 1/299,792,458 seconds. A meter is measured by the speed of light because 

1.  It remains constant everywhere.

2.  It can be measured from anywhere in the world to get an accurate and same result.

• In terms of Thermionic Emission: A krypton-86 atom in a vacuum emits orange-red electromagnetic radiation of a particular wavelength. Meter is defined as 1650 763.73 wavelengths of the radiation emitted by Krypton-86.

Other Units of Wavelengths:

As discussed earlier the SI unit of wavelength is meter. Some wavelengths are short and some are long. Even to solve different numerical problems the larger and the smaller units length was required. Thus we use exponential powers of 10 to measure the large property whereas the negative exponential is used for the measurement of shorter wavelengths.

Examples-

Submultiple Units: decimeter, centimeter, millimeter, etc

Multiple Units: decameter, kilometer, gigameter, etc.

Below is the table showing the relation of a meter with its multiple and submultiple units.

Multiples & Submúltiplos of SI Units - The Metre

The Relationship Between Wavelength and Frequency

Wavelength is the length of a wave and frequency is the number of waves. Thus in a unit area, if the length of a wave increases then its frequency decreases, and if the length of a wave decreases then its frequency increases. This means that the wavelength and frequency are inversely proportional to each other.

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Since the frequency of waves are measured in large units so wavelength (because it is inversely proportional to frequency) is measured in smaller units.

Wavelengths of Different Waves in Metres

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Gamma Rays: The wavelength of gamma rays is the shortest. It is less than 0.001 nanometer or 10-12 meters.

X-rays: The wavelengths of X-rays are in the range of 0.001 - 10 nm.

Ultraviolet: The wavelength of ultraviolet rays is in the range of 10 - 400 nm.

Visible Light: The wavelength of visible lights is in the range of 400-700 nm.

Infrared: The measure of the wavelength of infrared rays ranges from 700 nm to 1 mm.

Radio Waves: The wavelength of radio waves is the longest. It is longer more than 1 millimeter or 0.001 meters.

Practice questions based on Wavelength 

For a proper understanding of wavelength, let’s take a look at some of the practice questions based on the wavelength and frequency of a wave.

1. A radio station broadcasts at a frequency of 98, 400, 000 Hz. If the broadcast is an electromagnetic wave, then what would be the wavelength, if the speed of light is taken as c= 3 x 108 m/s. 

Answer: The relationship of the wave is denoted by the equation ƛ = c/f, where, 

ƛ= wavelength of the wave,

c= speed of light,

And, f = frequency of the wave. 

Substituting the given values to this equation leads to the following calculation:

ƛ = 3 x 10^{8} m/s / 98, 400, 000 Hz. 

  = 3.04 m. 

2. A note is played on the violin at a frequency of 445 Hz. If the speed of sound in the air is 345 m/s, what would be the wavelength of the sound?

Answer: the relationship between velocity, wavelength, and frequency is expressed by the equation of 

ƛ = velocity/ frequency.

Putting the values in the above mentioned equation, we get, 

ƛ  = 345 m/s / 445 Hz. 

= 0.77 m. 

Conclusion

Vedantu experts have covered all points and different features of Unit Wavelength. Students can use these solved examples to get practical knowledge.