"Shooting" is very common in both machinery and circuit.
The so-called "beat" refers to a low-frequency luffing signal synthesized by two sinusoidal signals with similar frequencies. The signal mentioned here can be either an electrical signal (electromagnetic vibration, usually called electromagnetic oscillation) or an acoustic signal (mechanical vibration).
The "beat" image generated by the synthesis of two sinusoidal electrical signals is shown in the following figure:
chart (1)
This is the simulation diagram. There are two independent voltage signal sources in Figure (1), one is 100Hz, the other is 110Hz. Observe the waveforms of the two voltage signal sources with two channels of the oscilloscope, and we can see two sine curves. Because the two sine signals have different periods, they vibrate in the same direction (such as the time indicated by the red arrow) and sometimes in the opposite direction (such as the green arrow The time indicated).
We can immediately judge that when the two voltage signals vibrate in the same direction, the combination of the two voltage signals must be superposition, and when the two voltage signals vibrate in the opposite direction, the two voltage signals must cancel each other. The voltage signal after synthesis must be changing in amplitude. It can be calculated that the frequency of amplitude change is exactly the difference between the frequencies of two sinusoidal voltage signals, as shown in the figure below.
chart (2)
It can be seen from the synthesized signal of two sinusoidal voltage signals with frequencies of 100Hz and 110Hz in Figure (2) that the waveforms at both ends of R1 are just as we expected, and the amplitude is constantly changing, and the frequency of amplitude change is 10Hz.
In Figure (2), the amplitudes of the two signals are the same, and the peak value of the composite signal varies between the sum of the amplitudes of the two signals and the difference between the amplitudes, so the waveform envelope at both ends of the composite signal R1 can reach zero. If the amplitudes of the two signals are different, the peak value of the composite signal still varies between the sum of the two signal amplitudes and the difference of the amplitudes, and the range of the peak values of the composite signal (including the average value during the two zero crossing periods, of course) is not so large, as shown in Figure (3).
Figure (3)
Is a new voltage signal generated after the synthesis of two voltage sinusoidal signals with different frequencies? Let's use the spectrum analyzer in the simulation software. Limited by the spectrum analysis software, and in order to see clearly, the frequency of the two sinusoidal voltages is changed to 1kHz and 1.1kHz, and the amplitude is also changed to 1.5V. The spectrum analysis range is 50Hz to 3kHz.
Figure (4)
Fig. (4) Spectrum analysis and simulation results show that there is no 100Hz component in the synthesized voltage signal, only 1kHz and 1.1kHz components.
So we can see in Figure (2) that the frequency of amplitude change of voltage signal after synthesis is the frequency of physical quantity change? It can be seen from Figure (2) that the peak voltage at R1 ends at the point pointed by the red arrow is close to 2V, the corresponding peak power is close to 4mW, and the average power between two zero crossings is close to 2mW (two sine signals with similar frequencies are not sine signals after synthesis, so they cannot be calculated as sine signals, but the difference is not far). The peak power on R1 where the green arrow points is close to zero, and the average power is also close to zero.
What is frequency? Frequency is the number of periodic movements of a physical quantity per unit time. Therefore, the frequency of signal amplitude change in Figure (2) is the frequency of average power dissipation change on R1.
Let's look at mechanical vibration again.
Figure (5) shows eight tuning forks made of steel. When you hit the tuning fork with a soft hammer (wood or hard rubber), the tuning fork will vibrate and make a sound. Each tuning fork is engraved with its frequency value. After the tuning fork is made, the frequency value is quite accurate, which can be accurate to 0.1Hz, and is less affected by temperature changes. The sound emitted by the tuning fork is gradually attenuated, but the attenuation is quite slow. It can last for tens of seconds or even longer in terms of the audible intensity of the human ear. Then it is difficult for the human ear to hear because the sound is too small. The characteristic of tuning fork vibration is very close to sine (the vibration beyond the fundamental frequency is very small), which is called pure tone in acoustics. Therefore, tuning fork is often used as sound source to emit sound of single frequency in acoustic experiments.
Figure (5)
If you hit the tuning fork, place it on a special wooden box with an opening at one end (the opening of the wooden box is on the left side of the figure), as shown in Figure (6), the sound of the tuning fork will become much louder, but the sound will decay faster.
Figure (6)
If we use two tuning forks, the frequency difference is very small, such as 1000Hz and 1001Hz. When we hit two tuning forks separately, we could not hear the difference in pitch between the two tuning forks. In other words, the difference between the vibration frequencies of two tuning forks is far less than the human ear's ability to distinguish pitch.
If we hit these two tuning forks at the same time, we will still hear a single tone. However, the size of the single tone, that is, the loudness of the sound, is changing from strength to weakness. The change frequency of sound loudness is exactly once a second, that is, 1Hz.
As we all know, the loudness of a sound means the power of the sound, and the "strong and weak" of the sound means that the power is changing periodically, so the "beat" of the sound is the frequency of the periodic change of the power.
In fact, the word "beat" originated from the study of people's voices.
By the way, when I was in the third grade of junior high school, the teacher in physics class once demonstrated to us the experiment of using two tuning forks with little difference in frequency to strike and vibrate to produce "beat frequency". We can clearly hear the changes in the strength of the sound, which is still fresh in our memory.
If the frequency difference between two tuning forks is large, such as 1000Hz and 1050Hz (this frequency difference is close to the "half tone" in music, which can be distinguished by ordinary people), the beat frequency when two tuning forks are struck at the same time is 50Hz. 50Hz is already audible to the human ear, but two tuning forks vibrate at the same time, and the human ear cannot hear the 50Hz sound. It just feels that compared with the sound emitted by a tuning fork, the sound is "unstable" and a little "shaking". In fact, this is what the human ear feels when the sound intensity changes at 50Hz.
Therefore, "beat frequency" is the frequency of periodic changes in the physical quantity of power.
If you have seen the inside of the piano, you will find that the string corresponding to each key of the piano is not one, but two or three strings corresponding to each key side by side. When each key on the piano is pressed, a small wooden hammer covered with felt is driven by a set of levers (string striking machine) to strike the two or three strings.
When piano tuners tune the piano, some tune the two or three strings corresponding to the same key to the same pitch, and some tune the two or three strings to a slightly different pitch. This "little difference" will produce a beat frequency, making the sound of the piano completely consistent with the three strings and different, with a "beat" effect, and the sound has some "tremor", which creates a special timbre.
However, the sound "tremor" produced by the piano is not as strong as that produced by two tuning forks with very similar frequencies. This is because the sound produced by the piano is not pure sound, that is, it is not a sine wave, but a sound containing a lot of harmonics. When two strings vibrate, the fundamental waves just strengthen each other, but the second harmonic waves do not necessarily strengthen each other, which is likely to cancel each other. When the fundamental waves cancel each other, the second harmonic waves may strengthen each other, as well as the third and fourth harmonic waves, so the "beat", that is, the sound loudness changes little. Well trained tuners can recognize (often tune on this basis), but ordinary people often can't recognize "beat frequency", just feel different timbre.
Each key on the right hand of the larger keyboard accordion corresponds to two reeds. When the air current blows the two reeds, the fundamental sound frequencies produced by the two reeds are different, with a difference of several Hz. This will also produce a "beat frequency", resulting in a tremolo effect, and also a special tone color of the accordion. The Russian button accordion, Bayan, has only one reed for each button on the right hand keyboard, so there is no vibrato caused by beat frequency. Therefore, the tone of the Russian accordion is different from that of the ordinary accordion and unique.
When it comes to "timbre", it was early believed that different timbres were caused by different harmonic content. For example, the empty string of the guitar, the plucked string near the middle of the string and the plucked string near the root of the string, sounds the same pitch to the human ear, but can distinguish the two sounds are not the same. If you haven't played guitar before, just ask around@ Computer00 Because the harmonic content of the sound produced by the two plucking modes is different, people believe that different timbres are caused by different harmonic content.
Later, it was found that the two vibrations whose frequencies were not too different sounded like a single tone, but the "flutter" caused by the beat frequency also caused different timbres. This point has been described previously.
Later research found that when hearing different instruments, such as violin and flute playing the same pitch, it is easy to identify which instrument is playing. Obviously, the timbre of the two instruments is different. However, electronic technology is used to remove the beginning and end of this sound, leaving only the middle part, which is difficult for the human ear to distinguish, and no difference can be heard. Then, the "head" and "tail", that is, the unstable state at the beginning and the unstable state at the end of the vibration, will also affect the timbre. Both the harp and the guitar are plucked instruments, but the sound timbre of the harp and the guitar is different, which can be easily distinguished. This is because the strings of the harp and the guitar are fixed in different ways.
It can be seen that timbre is very complex and has a lot of subjective elements.
