Why does a longer string make a lower note when it vibrates?
Quick answer
For a string fixed at both ends, the fundamental vibration has a wavelength twice the vibrating length. If wave speed stays the same, making that length longer also makes the wavelength longer and the frequency lower, so the note sounds lower. But length is not the only factor: tension and mass per unit length affect wave speed, and therefore affect frequency too. [S1] [S2]
The question, the details, the next step.
Why does a longer string make a lower note when it vibrates? I get that it has more room to move, but I don’t see how that changes the sound.
Think of the string as making a repeating wave pattern while its ends stay fixed. For the simplest pattern—the fundamental—half of one wavelength fits along the vibrating length. So a longer vibrating section has a longer wavelength in this pattern. Frequency is how many wave cycles happen each second; if wave speed is unchanged, a longer wavelength means fewer cycles per second and a lower fundamental frequency. That is why the note is lower. [S1] [S2]
The important length is the part of the string that is free to vibrate, not necessarily the total length of string.
So does shortening a string always make the note higher? What if I press it down on a fret?
Shortening the section that can vibrate raises its fundamental frequency when the string’s tension and mass per unit length stay the same. In a fretted-string example, pressing the string against a fret shortens the vibrating section; under that comparison, the shorter section produces a higher fundamental.
The word “always” needs a qualification: if tension or the string’s mass per unit length also changes, length alone cannot predict the pitch. For a simple comparison, use the same string and keep its tension as steady as possible.
You mentioned tension and the string’s mass. How do those fit in without making this too complicated?
They affect how quickly a wave travels along the string. For an ideal stretched string, wave speed depends on tension and linear density—mass per unit length—according to v = √(T/μ). Frequency depends on that wave speed as well as the wavelength. [S1]
If tension increases, wave speed increases; if mass per unit length increases, wave speed decreases, assuming the other quantity stays the same. Those changes affect frequency and pitch too. The relationship explains how the factors interact, but it does not give an exact note without the string’s relevant properties and vibrating pattern. [S1]
Can you give me a simple way to explain it to a child, or to check the idea with a string?
You could say: “A short vibrating section can complete more wave cycles each second, so it makes a higher note. A longer section has a longer wavelength and, if the wave speed stays the same, completes fewer cycles each second, so it makes a lower note.” [S2]
For a simple comparison, use one string and change only how much of it is free to vibrate. Keep the rest of the setup as consistent as you can, and listen for the change in pitch. Treat it as a comparison, not a precise measurement: the explanation assumes the fundamental vibration, and tension and mass per unit length also affect the result. [S1] [S2]
A practical checklist
Identify the vibrating section, rather than just the total string length.
For a length-only comparison, use the same string and keep tension as steady as possible.
Explain that the fundamental’s wavelength is twice the vibrating length.
Connect a longer wavelength at unchanged wave speed to a lower frequency and pitch.
Mention that tension and mass per unit length also affect wave speed and pitch.
A few more useful answers
What does “fundamental” mean here?
It is the simplest vibration pattern of the string, with half a wavelength fitting along the vibrating length. The explanation about length lowering pitch is specifically about this mode. [S2]
Is pitch determined by length alone?
No. The comparison assumes tension and mass per unit length stay the same; both affect wave speed and therefore frequency. [S1]
Can this explanation tell me the exact note a string will make?
Not by itself. It explains how length, wave speed, and wavelength relate, but an exact pitch requires details about the string and its vibrating conditions.
Sources
References used for this guide.
- [S1] OpenStax University Physics Volume 1: Wave Speed on a Stretched String openstax.org · Checked
- [S2] OpenStax University Physics Volume 1: Standing Waves and Resonance openstax.org · Checked