

Introduction to Beat Waves
Physics is applicable everywhere. Every action that we undergo will definitely have an idea of Physics behind it. We were aware of the concept of sound and its various formats such as in the form of noise, melodious such as the sound of any musical instrument, etc. Using the concept of beats many musical instruments have been developed. Even a minute change in beat can result in an extraordinary tune. Beat waves are not only used in the music industry but also in the medical field. These days, in order to treat many neural disorders, doctors use beat wave therapies.
To produce a melodious tune or song, the musician needs their instrument to have the correct sound. They produce the desired frequency by adjusting the equipment and try to match it with their instrument’s frequency. If the two frequencies are not matching, they will interfere to produce alternating loud and soft sounds.
A sound wave not only propagates in space but also can propagate through time. Thus, if the two sound waves can produce interference by overlapping in space, they should also be capable of producing an interference pattern when they overlap in time. This phenomenon is called beats and the waves are known as the beat waves.
Gamma Binaural Beats
Beats occur when two waves of nearby frequencies overlap and create a new resultant wave. Using the same idea of producing beat waves not only music but can also be utilised in the field of medicine for curing many neural disorders. One among such treatments is gamma binaural beats therapy. Even before we start with gamma binaural beats therapy, let us understand what we mean by binaural beats.
Basically, the binaural beats are of the two different types of beat waves with different frequencies that are heard separately, one in each ear. Our brain is capable of processing the difference between these two beats to understand the difference between the frequencies. Binaural beats are certainly dangerous as they can cause noise-induced hearing loss which will ultimately result in permanent loss of hearing over a period of time. Binaural beats in sound waves is an auditory phenomenon in which the eardrum ruptures or the middle bone in the ear can get damaged.
Now, binaural beat therapy is an emerging form of sound wave therapy that is found to be having a high success rate. Binaural beats waves therapy utilizes the fact that the right and left human ear each receive a slightly different frequency tone, yet the brain perceives and processes these dissimilar frequencies as a single tone. Binaural therapy is currently being recommended for the treatment of anxiety, stress, and related disorders that are found to occur mostly in all age groups. Binaural therapy is actually a self-help treatment and it is usually available in the form of audio recordings that a person listens to on stereo headphones.
Now, the gamma binaural beat therapy, as the name itself suggests here we will be using gamma waves to treat neural disorders. This is also known as the gamma pattern in medical terms and gamma binaural beat therapy, the frequency pattern accounts for a range of 30–50 Hz. The study of many doctors and scientists suggest that these frequencies promote the maintenance of arousal while a person is awake.
As the leading authorities in psychiatric treatment have no recommendations for binaural beats, it is usually the producer of the tape that makes the suggestions for use. People should follow the instructions carefully before they start with gamma binaural beat therapy, delta binaural beats (or binaural beats delta waves) or beta binaural beats therapy. Those who do not find any difference or do not notice any reduction in anxiety might benefit from trying a different producer, type of sound, or frequency. It is most important to avoid using gamma binaural beats therapy or any other binaural therapies while undertaking tasks that require alertness and full attention.
Beats in Sound Waves:
Now, how do the beats in sound waves are produced? Let us understand with an example, consider two beat waves with two different frequencies f\[_{1}\](say purple) and f\[_{2}\](say green). The waves are interfering constructively in the green highlighted regions, leading to a larger amplitude when the waves combine in f\[_{B}\]. The white highlighted regions are where destructive interference occurs, and the amplitude of f\[_{B}\], is smaller than the original sound waves. The variation in amplitude results in the alternating volume or the loudness of sound that we call beats or beat waves.
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Let us consider another example, for understanding how beats in sound waves are produced. We will need two tuning forks (turning fork) of close frequencies e.g. 800Hz and 850Hz. Both the frequencies are almost identical and there is no major or intense difference in the audible frequency. You hear when you play each of them individually, but when played together these two frequencies, they will overlap with each other, as they are very close to each other in terms of frequencies and their crest to crest interference produces a constructive interference and which in turn results in the increase of the amplitude of the wave hence the loudness of sound increases, resulting in the production of beat waves.
When a crest to trough meet the resulting interference will be destructive in nature, hence they both will end up cancelling out each other and thus the amplitude produced will be equal to zero. Hence the loudness will suddenly drop to zero or reduce to zero. The frequency at which the intensity of the loudness increases and decreases is known as the beat frequency. This beat frequency is always equal to the difference between the two frequencies which produced it. This is how the beats in sound waves are formed.
Did You Know?
We know that all matter is made of small particles known as molecules. When a sound wave is generated, the molecules end up bumping into one another in a particular pattern. Those molecules bump onto the next set of molecules, which in turn bump into the next molecules and so on. This collision continues until the energy runs out. The best example can be, have you ever thrown a rock into a pond, then we will notice the rings of water waves that move out from the place where the rock landed. This is much the similar way that sound waves travel.
One of the most important things to remember about the wave motion of the particles or the waves is that they transport energy, not matter. This criterion makes them different from another phenomenon in physics.
The finest and tallest ocean wave ever witnessed and recorded was 1,720 feet tall and occurred in Lituya Bay in Alaska.
The Doppler Effect is experienced when the sound waves from the moving object are moving toward the observer, i.e., under the relative motion. As the object moves closer to the observer, the distance between the object and the observer gets shorter. Because of this decreasing distance, the sound waves are being compressed between the two, i.e., between the object and the observer. As the object moves further away from the observer, the distance increases and it takes longer for the sound to reach them. The sound then appears to be lowered. The actual frequency of the sound wave never actually varies.
FAQs on Beat Waves
1. What are beat waves in Physics?
In Physics, beats are the periodic and repeating fluctuations in the loudness of a sound that occur when two sound waves of slightly different frequencies interfere with each other. The resulting sound wave has an amplitude that varies over time, causing the sound to be perceived as waxing and waning in intensity. This phenomenon is a specific example of wave interference in time.
2. What is the underlying principle that causes beat waves?
The formation of beat waves is governed by the principle of superposition. When two waves with nearly equal frequencies travel in the same medium and overlap, their displacements add up at every point. This leads to:
- Constructive Interference: When the crests or troughs of both waves align, their amplitudes add up, resulting in a louder sound.
- Destructive Interference: When the crest of one wave aligns with the trough of the other, their amplitudes cancel out, resulting in a softer sound or silence.
This alternating pattern of constructive and destructive interference creates the characteristic 'beating' sound.
3. How is beat frequency calculated?
The beat frequency is the rate at which the loudness of the sound varies. It is calculated as the absolute difference between the frequencies of the two interfering waves. The formula is:
fbeat = |f₁ - f₂|
Here, f₁ and f₂ are the frequencies of the two individual waves, and fbeat is the number of beats heard per second, measured in Hertz (Hz).
4. What are some practical applications of beat waves?
The phenomenon of beats has several important real-world applications. Some key examples include:
- Tuning Musical Instruments: Musicians listen for beats when comparing an instrument's note to a reference frequency. They adjust the instrument until the beats disappear, indicating the frequencies are perfectly matched.
- Detecting Dangerous Gases: In mines, special pairs of whistles are used. When a dangerous gas enters the air, it changes the speed of sound through one whistle, creating audible beats that serve as a warning.
- Medical Therapies: Binaural beats are used in sound wave therapy to try and induce specific mental states, such as relaxation or focus, by playing slightly different frequencies into each ear.
- Radar Speed Guns: Police radar guns use the beat frequency between the outgoing and reflected radio waves (Doppler effect) to determine a vehicle's speed.
5. What is the difference between interference and beats?
While beats are a result of interference, the two concepts are distinct. The primary difference lies in the conditions and the resulting pattern:
- Interference is a general phenomenon where two or more waves superpose to form a resultant wave. It often refers to a stationary pattern of high and low intensity created in space (e.g., the bright and dark fringes in a light experiment). This typically involves waves of the same frequency.
- Beats are a specific type of interference that produces a variation of intensity over time at a particular location. This phenomenon specifically requires the two interfering waves to have slightly different frequencies.
6. Why are beats only audible when the interfering frequencies are very close to each other?
The human ear can only perceive the periodic rise and fall in loudness as distinct 'beats' if the beat frequency is low, typically below 10-15 Hz. If the difference between the two source frequencies (|f₁ - f₂|) is large, the beat frequency is too high for our brain to process as a rhythmic pulse. Instead of hearing beats, we perceive a rough, discordant sound or simply hear the two separate tones simultaneously.
7. How do musicians use the phenomenon of beats to tune their instruments?
Musicians use beats as a highly accurate auditory tool for tuning. The process involves:
- Playing a reference note from a trusted source, like a tuning fork or an electronic tuner.
- Playing the same note on the instrument that needs to be tuned.
- If the instrument is out of tune, the two slightly different frequencies will produce audible beats.
- The musician then adjusts the tension or length of the string/pipe, listening carefully to the beat frequency. A slowing of the beats indicates they are getting closer to the correct pitch.
- The instrument is considered perfectly in tune when the beats disappear completely (i.e., the beat frequency becomes zero), signifying that both sources have the exact same frequency.
8. What is a 'beat period' and how does it relate to beat frequency?
The beat period (Tbeat) is the time interval between two consecutive moments of maximum loudness or two consecutive moments of minimum loudness. It is the time for one full cycle of the beat pattern. The beat period is the mathematical reciprocal of the beat frequency. The relationship is given by the formula:
Tbeat = 1 / fbeat
This means that a higher beat frequency (more beats per second) corresponds to a shorter beat period (less time between each beat).

















