Beat is a phenomenon that occurs with waves. Above all, the beating is an important part of the acoustics. In this article we explain everything about beating. The topic is part of the theory of waves and belongs to the subject of physics.
What is the beat?
In physics, beat describes a certain effect. If the resultant of the additive superimposition of two oscillations has a periodically increasing and decreasing amplitude, this is called beat. The frequency of the two oscillations differs only slightly from one another. The additive superposition is also called superposition. You can read more about this topic in the article on interference.
The resulting wave has an increasing and decreasing amplitude. This is because the instantaneous values of the output oscillations periodically reinforce or weaken each other depending on the phase shift. The greater the difference in the output frequencies, the higher the frequency of this change.
The instantaneous value simply describes the value of a time-dependent variable at a given point in time. The term phase shift was also explained in more detail in a separate article. To get to it, just click on the term.
No new frequencies are generated during the beating and no frequency shifts occur either. The figure below shows an example of a beat between two frequencies. Above you can see the two output frequencies in blue and pink, below is the beat that was formed by adding the two above curves.
via wikipedia.org
- If the resultant of the additive superimposition of two oscillations with only slightly different frequencies shows a periodically increasing and decreasing amplitude, this is called beat.
- No new frequencies are generated during the beating and no frequency shifts occur either.
In which waves do beats occur?
Beats occur in all waves for which the principle of superposition applies. As already explained in detail in the article on interference, the principle of superposition describes the undisturbed superimposition of several waves of the same type. The principle of superposition applies, for example, to sound waves, electromagnetic waves or electrical signal currents.
- Beats occur with all waves for which the principle of superposition applies, e.g. sound waves, electromagnetic waves or electrical signal currents.
The beating in acoustics
Two tones of the same volume are vibrations with the same amplitude. If two such tones are produced with slightly different frequencies, our ears do not perceive these two tones separately. We only hear a rising and falling of a tone whose height roughly corresponds to the height of the starting tone. This phenomenon is called beating.
In addition, the resulting tone is modulated and its volume varies with the beat frequency, which is the difference in the frequencies of the two tones. The beat frequency is discussed in more detail later in the article.
- In the case of two tones of the same volume with slightly different frequencies, our ears only perceive an increase and decrease of the tone.
- For us, the newly created tone roughly corresponds to the volume of the initial tone and fluctuates with the beat frequency.
The superposition oscillation
If two tones with slightly different frequencies are heard, a tone can be heard whose frequency corresponds to the mean value of the frequencies of the two superimposed tones. The tone is also referred to as a superimposed vibration. The frequency of this oscillation is denoted by fR. It is calculated by taking the arithmetic mean of the two output frequencies. So the formula is as follows:
fR = (f1 + f2) / 2
f1 and f2 each stand for the frequencies of the two superimposed tones.
- The superimposed oscillation is calculated using the arithmetic mean of the two output frequencies.
The frequency of the envelope
The amplitude of this local oscillation varies with the frequency, which is denoted as fS. This quantity is also called the frequency of the envelope. It is calculated using the formula fS = (f1 – f2) / 2
The beat frequency
The frequency of the envelope fS is usually much lower than the frequency of the superimposed oscillation fR. The beat frequency describes the frequency with which the magnitude of the envelope changes.
The beat frequency can be calculated by the amount of difference between the frequency of tone 1 and the frequency of tone 2.
- The beat frequency is the frequency at which the magnitude of the envelope changes.
How are these values of the beating related to each other?
So if two tones are heard whose frequencies differ only slightly, a tone of frequency fR can be heard. This tone is not always the same volume, but fluctuates with the beat frequency f. The closer the two output frequencies are to each other, the slower the volume of the resulting oscillation swells up and down. In addition, the frequency of the envelope is lower, the closer the two output frequencies are to each other.
- The frequency of the superimposed oscillation fR occurs when two tones with slightly different frequencies are superimposed.
- This tone varies with the beat frequency.
- The lower the frequency of the envelope, the closer the two output frequencies are to each other.
What is the phenomenon of beating used for?
Beat is an important phenomenon that is used in many ways. For example, in music-making practice, beating is often used. If a musical instrument is tuned by ear, it is tuned in until no more beats can be heard. One then speaks of a tone that is zero-beat. The beating is also used as an invigorating sound effect on musical instruments, such as the accordion or a pipe organ.
Another example of an area where beating is used is shipping. Shipwrecked people are usually given a whistle that emits particularly low tones. This is because low-pitched sounds can be heard farther than high-pitched sounds. However, if you want to produce a deep tone directly, the whistle would have to be made unwieldy in size. By superimposing two tones, it is possible to generate a low-frequency oscillation with the beat frequency.
- In music, beating is used, for example, to tune musical instruments or to create invigorating sound effects.
- In order to generate deep tones that can still be heard from afar, the beating must be used.
Everything you need to know about beating at a glance:
- If the resultant of the additive superimposition of two oscillations with only slightly different frequencies shows a periodically increasing and decreasing amplitude, this is called beat.
- Beats occur with all waves for which the principle of superposition applies, e.g. sound waves, electromagnetic waves or electrical signal currents.
- In the case of two tones of the same volume with slightly different frequencies, our ears only perceive an increase and decrease of the tone.
- The superimposed oscillation is calculated using the arithmetic mean of the two output frequencies.
- The frequency of the envelope is the frequency with which the amplitude of the local oscillation varies.
- The beat frequency is the frequency with which the magnitude of the envelope changes.
- The beating is used in a wide variety of areas, such as in music-making practice.