Firstly, we need to understand the attenuation characteristics of sound in the air. In general, sound travels farther in the air at low frequencies than at high frequencies. A typical example is during thunderstorm season, when we hear distant thunder, it is usually a low, rumbling sound. And the nearby mines are very sharp and piercing. That is to say, in the air, the propagation of sound follows this pattern: the higher the frequency or the higher the pitch commonly mentioned in music theory, the easier it is to attenuate. Zoologists have found that elephants can even communicate with lower frequency and less easily attenuated infrasound roars, which can travel for tens of kilometers.

Secondly, we need to understand the essence of the unique timbre of the violin, which is actually the generation of rich harmonics based on the fundamental frequency. The effective intensity can be extended to around 8 kHz. However, in reality, the fundamental frequencies of the notes produced by the violin are mostly concentrated between 196 and over 800 hertz. Except for the high pitch, other frequencies of sound waves are integer multiples of the fundamental frequency, commonly known as "homophones". The intensity distribution of homophones in different multiples is uneven, and each qin is different. The combination of different intensities of these homophones constitutes the "timbre".

Alright, once you understand the above two questions, the mystery of penetration power will be revealed.

For example, use two hypothetical pianos with different timbres: one is the A piano with more high-order harmonic components, and the other is the B piano with less high-order harmonic components. The performer uses the same force to move the bow and excite the four strings to play a piece of music with evenly distributed high and low notes. Assuming we are active listeners who constantly distance ourselves from the performer, imagine which instrument has a stronger sound in the distance? Is it an A piano or a B piano?

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If you have carefully considered and understood your life experience with thunder, I believe you would definitely choose the B Qin!

As mentioned above, the performer used the same passion and strength, that is, the same energy, to excite the strings. The A piano has more energy allocated to higher-order harmonics. Due to energy conservation, the energy allocated to the fundamental and lower order harmonics is reduced, and the high notes are rapidly attenuated. As the distance increases, the sound of the piano becomes weaker. Similarly, the sound intensity of B piano attenuates less at a distance, so it naturally has stronger penetration.

But timbre really belongs to the realm of aesthetic psychology. A truly penetrating instrument may sound like a sound stuck in a pot up close, which is a very subtle feeling. After a while, it becomes a horsehead fiddle or erhu and loses the characteristics of a violin. Without a little pot bottom sound, it loses its penetrating power.