Wavelength to Frequency Formulas - Definitions & Practice Questions
Wavelength and frequency are two important characteristics to explain the nature of a wave. Wavelength is basically the measure of the distance between two successive points referred to as crests or troughs of a wave. It is always measured in the direction of the wave and is represented by the symbol \[\lambda \]. Since it is a measure of the length of distance, it is expressed a unit of length, i.e., meters. Mathematically, it is the speed of the wave in a medium divided by the frequency of the wave.
Frequency of a wave is the number of occurrences of events per unit time. Mathematically, it is the reciprocal of the time period. Frequency is represented by the symbol ‘f’ and its unit is Hertz (Hz). In the context of waves, it can be defined as the number of waves that can pass a certain fixed point per unit of time.
Relationship Between Wavelength and Frequency
The wavelength of a wave is inversely proportional to its frequency. If v represents the velocity of a wave, its frequency f, and its wavelength\[\lambda \], then;
\[\lambda = \frac{v}{f}\]
This means, as wavelength increases, the frequency will decrease and vice versa.
In the case of light in a vacuum, this formula is given as \[\lambda \]=cν
Practice Questions:
Example 1: A typical sound wave traveling at 360 m/s has a frequency of 1200 Hz. Find its wavelength.
Solution:
\[\nu \] = 1200 Hz, v = 360 m/s, \[\lambda \]=?
\[\lambda = \frac{v}{\nu } = \frac{{360}}{{1200}} = 0.3\,m\]
Example 2: All electromagnetic waves travel through a vacuum at the same speed. If a wave of frequency 7.5 GHz has a wavelength of 4 cm, then the frequency of a wave with wavelength 6 km will be (assume both are electromagnetic waves propagating in vacuum):
Options:
40 kHz
50 kHz
5 GHz
2.5 MHz
Answer: (b)
Conclusion
Vedantu provides the concepts of Wavelength and Frequency and helps you in solving the questions in an elaborate manner. You can find everything you’re looking for in PDF format in one place through Vedantu. In the PDFs, which are also downloadable for free, students can go through concepts of wavelength and Frequency, their Definitions, relationship, and questions carefully and understand the concepts used to solve these questions. This will help the students immensely in their examinations.
FAQs on Wavelength to Frequency Formula
1. How are the wavelength and frequency related to each other?
The speed of a wave is mathematically the product of the wavelength and frequency of the given wave. This speaks about the relation between the wavelength and frequency of the wave. If frequency increases then the wavelength will decrease. So, they are basically inversely proportional to each other. The characteristic of an electromagnetic wave is that it has a definite speed and that is equivalent to the speed of light, which is constant. Hence, this implies that for a wave having a longer wavelength it has a low frequency and vice versa. Vedantu provides all the solutions and concepts in a systematic way on its website for your better understanding.
2. What is the importance of knowing the wavelengths of a wave?
One of the important characteristics of a wave is its wavelength and it has several applications in research in the field of physics, spectroscopy applications in Precision Agriculture, and also in airborne instrumentations. The wavelength of a wave can give an idea about the nature and type of waves, be it sound-wave or light-wave. To study tidal waves, an earthquake, or any other normal phenomenon the concept of wavelength is extremely necessary. To determine the speed with which a wave will travel propagate and with what frequency and amplitude the concept of wavelength are very important. Vedantu provides all the solutions and concepts in a systematic way on its website for your better understanding.
3. How many types of electromagnetic radiations are there based on wavelengths?
Depending upon the length of waves they are mainly classified into the following seven types of waves. There are several wavelengths but the main types of electromagnetic radiations based on the value of their wavelengths, energy, and frequency are listed below:
Radio Waves, which have a long wavelength and low frequency are used in the broadcast of radio, navigation, air traffic control, military communication and television, and many remote-controlled devices and toys.
Microwaves with a wavelength ranging from one meter to one millimeter. This is these are used in communication links including; spacecraft communication, cancer treatment, in microwave ovens to heat foods, and even reactions using thermal energies.
Infrared Waves have wavelengths ranging from one millimeter to seven hundred nanometres. It is used in medical applications, night light devices, and in many scientific and military devices.
Optical waves are used in astronomy, oceanography, in industries to measure refractive indexes and surface irregularities. The wavelength of optical waves varies from hundred nanometres to one millimeter.
Ultraviolet waves are used for killing bacteria and other microorganisms, photography, water purification, UV lamps, production of Vitamin D, and many more purposes. The range of wavelength is between ten to four hundred nanometers.
X-rays have wavelengths between 0.01 to 10 nanometres. They are of a much shorter wavelength and are used in the medical field for detecting fractures, stones, tumors, and also to do chest x-rays and mammography.
Gamma rays, which have the shortest wavelength among all the mentioned ones, are as small as one-tenth of angstrom. It has applications in radiation therapy for cancerous cells.
The longest wavelength is of radio waves while the shortest is the gamma-ray. They are arranged in a descending fashion. Vedantu provides all the solutions and concepts in a systematic way on its website for your better understanding.
4. What are the theories of a light wave?
The theory of the light proposed by Christian Huygens, explains that light is of wave nature. The other theories which establish this wave theory are as follows:
Electromagnetic nature of the wave proposed by Maxwell.
Dual nature of light by De Broglie, which explains both the particle and wave nature of light.
Briefly, the theories explain that light has a wave nature apart from its particle nature and every point within a wave is an origin of a secondary wavelet. Vedantu provides all the solutions and concepts in a systematic way on its website for your better understanding.
5. Which has more energy, an electromagnetic wave with higher frequency or higher wavelength?
The energy of an electromagnetic wave is directly proportional to the frequency provided other variables are kept constant. On a similar note, the energy of a wave is inversely proportional to the wavelength. Both these statements are justified by the following equations:
Energy = Planck’s constant * Frequency
Energy = (Planck’s constant * Speed of light) / (Wavelength of the wave)
Thus, if other variables are kept constant then a wave with a higher frequency possesses more energy than the one with a higher wavelength.
The practical significance of this concept is felt in the field of radiology and radiotherapy, where high-frequency waves are used to locally burn or cauterize a particular tissue or lump inside the body without any surgical incision. This procedure is called radiofrequency ablation. Vedantu provides all the solutions and concepts in a systematic way on its website for your better understanding.