An FM Radio Station Broadcasts At A Frequency Of 101.3 Mhz. What Is The Wavelength?

Wavelength Interesting Problem!

The wavelength is an important datum, since, when studying the way in which information is transmitted through radio frequencies, it will depend on how easily the signal will cross obstacles. A good aspect of radio frequency is that despite the objects or buildings that can obstruct the waves, there are always ways to modify the frequencies to improve the flow through the objects.

Waves can be simulated as a sinusoidal function. A sinusoidal function that describes the wave can be seen as follows:

wavelength of a sine wave

We see that the red color curve represents an alternation, which, the faster or shorter it is, indicates a higher frequency of the waves, in addition to the λ value, which represents the length of the wave. Knowing a little about wavelength, we can proceed with the problem to solve.

The Wavelength Equation

The wavelength equation is an equation that relates 2 variables, one that indicates the frequency and the other that represents the transmission speed of the wave, so that a wavelength is a physical unit of distance or measure.

The reason why frequency is used as an influencing variable in the wavelength formula is that frequency tells me how close the inflection points are to each other, that is, how close the local minima are to each other and the same with local highs. The other variable, the transmission speed, is a unit that indicates how far to travel in a certain unit of time, with meters “m” being the unit that prevails in the result.

The equation has the following form: λ=v/f

wavelength equation

Where v is the speed of propagation of the wave and f is the frequency. The value v is the speed of light, because in the case of electromagnetic waves, the lowest part of the spectrum is the radio frequencies used in current communications, and these waves travel at the speed of light. With this equation, we can solve the following problem: An FM radio station broadcasts at a frequency of 101.3 MHz. what is the wavelength? We already have the frequency, we already know the speed of light by default, which is 3×108 m/s now let’s see the solution:

wavelength solution

We see that the wavelength has a value of 2.96 meters, which indicates that the frequency of the signal is low because according to the sinusoidal curve, it is a large distance between each cycle of the wave.

cycle of the wave

This is a very important piece of information, here we can realize that, despite the fact that there is an obstruction in the path of the wave, as it has a great length, it can cross obstacles more easily, without altering the frequency or performance of the waveform. data transfer.

Importance of achieving a suitable wavelength

Thanks to the fact that the wavelength can be controlled to a certain extent, great important technological developments have been achieved. One of them was 5G technology, which has recently hit the market, taking telephony technology to another level.

The waves generated by equipment that facilitated the 4G network, the frequency readings were below 6GHz, but the enormous difference with 5g is that it is included in the range of 30 GHz to 300GHz, which are very low frequencies and very wavelengths are small, so waves can pass through almost anything without much interruption. This will promote the advancement of many new technologies, such as the so-called internet of things.

An incredible comparison between the 4G and 5G networks is the difference between the data download speed limit and latency. While the 4g + network can reach 1200 Mbps at a latency of 20 milliseconds, the 5G can reach the amazing speed of 10000 Mbps with an almost immediate latency of 1 to 2 milliseconds, that is, the access to the network will sometimes be faster than accessing local documents on a computer.

Another example of the great importance of wavelength: is the laser

One of the most important applications of the wavelength is the implementation of the laser beam in different areas of medicine and in the design of machines. We will see some types of Lasers according to their wavelength, in addition to some applications they have in the field of medicine:

  • Red laser: The wavelength of this type of laser is 600 to 660 NM. This type of laser causes energy to be absorbed close to the surface of the skin, in the case of medical applications, which is excellent for treating scars or burns, including cosmetic problems.
  • Near-infrared laser: it has a wavelength of 800 to 850 NM. It is the best length for treatments that can be applied by means of a laser beam. This frequency allows good interaction with cells, including a good interaction with mitochondria. This type of laser promotes the formation of substances that promote healing, such as cytochrome C, oxidase, and adenosine tri-phosphate. This is one of the lasers most used today, due to the frequency balance, which allows multiple applications.
  • Pulsed laser: The wavelength of this laser is approximately 905 NM. This laser has a good wavelength for cellular interaction, but it must be managed by turning off and on the led generated by the laser, since, due to prolonged exposure, it can cause damage to tissues such as the eye. The length of this type of laser promotes the interaction with the iron in hemoglobin, at the same time that it oxygenates the area through this process. As a certain area being treated is oxygenated, this leads to better healing.

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The previously exposed topic gives us an overview of the importance of physics in development. If there was no way to measure the wavelength, it would be very difficult to detect the benefit or the damage that the waves are causing to equipment and people, as well as the example of the Pulsed laser, because knowing that its wavelength is so large, it must be supplied with an LED that turns on and off constantly. There are multiple applications to the calculation of wavelength, it all depends on what you want to achieve.


What color is the longest wavelength?

Human eyes cannot see the longest wavelength. The wavelength of ~700 nm is the longest that we can see and its color is red.

How do you calculate energy from wavelength?

First, you need to convert the wavelength into meters, and then you divide the speed of light (3×108 m/s) by this wavelength to get the frequency. For last you multiply that frequency by Planck’s constant, (6.626 x 10-34) and the result is the wave’s energy (in Joules)

Read More: How to Cite a Radio Broadcast?



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