不同介质（含非地球大气）中振动琴弦的泛音列是否存在差异？

Great question—this dives into the cool overlap of physics and music theory, so let’s break it down clearly for you.

Do the characteristics of the overtone series come from the interaction between the string and its medium? #

Short answer: No, the core structure of the overtone series is inherent to the string’s own vibration patterns, but the medium is critical for us to actually perceive those overtones.

Here’s the breakdown:

• When you pluck a string, it doesn’t just vibrate as a single whole (producing the fundamental frequency). It also vibrates in segmented chunks—1/2 its length, 1/3 its length, 1/4 its length, and so on. Each of these segmented vibrations creates a frequency that’s an exact integer multiple of the fundamental (2x, 3x, 4x, etc.)—that’s the overtone series.
• These vibration modes are determined purely by the string’s physical properties: its length, tension, and how much mass it has per unit length. The medium (like air) doesn’t create these modes—it only carries the string’s vibrations to our ears (or a microphone). Without a medium, you wouldn’t hear the overtones, but the string would still vibrate with those same overtone patterns.

Would the overtone series of the same string show essential differences in different atmospheric environments or other media? #

Again, the defining structural trait of the overtone series (integer multiples of the fundamental) won’t change, but how we perceive the overtones (and how they travel) will shift a lot.

Let’s break this down for common scenarios:

• Different Earth atmospheric conditions: Changes in temperature, humidity, or air pressure alter air density and sound speed. This affects the relative loudness of individual overtones (some frequencies might be absorbed or amplified more than others) and how fast the sound fades. For example, dry air soaks up higher overtones faster than moist air, making the sound feel "darker." But the overtone frequencies themselves will still be exact integer multiples of the fundamental—no essential shift to the series’ structure.
• Other media (e.g., water, helium): In denser media like water, sound travels way faster, but the string’s vibration modes stay the same. The fundamental and overtones are still proportional integer multiples. What changes is the timbre (tone color) of the sound, since different media carry different frequency ranges with varying efficiency. In helium, for example, sound moves quicker, but the string’s overtones still follow the integer rule—your perception of pitch might warp if you’re listening through helium, but the overtone series’ core structure doesn’t change.
• Vacuum: In a vacuum, there’s no medium to carry vibrations, so you can’t hear the string at all. But the string still vibrates with its inherent overtone modes—you just can’t detect them without a medium to transmit the energy.

The big takeaway: The overtone series’ signature integer-multiple frequency relationship is a property of the string itself, not the medium. The medium only affects how we experience those overtones, not their fundamental structure.

内容的提问来源于stack exchange，提问作者conner.xyz