Musical instruments
27 More about strings
What are guitar players doing when they move the left hand around and press a finger down? What do the tuning pegs do? Why do starting violin players sound screechy? Why do string instruments usually have several strings of different thicknesses? This section will apply the standing wave model for strings to answer these and other questions about playing string instruments.
Anatomy of a string instrument
String instruments across many cultures share many elements- a body, a fingerboard, tuning pegs, a tailpiece, a bridge, a nut. At the heart of the instrument is the string. Each string is anchored to a tailpiece at one end of the instrument. From there, the string passes over the bridge, then over the nut and then is wound around a tuning peg. Only the part of the string between the bridge and the nut is meant to vibrate.
Open strings
If the player plucks or bows the string without touching the string with the other hand, the part of the string between the nut and the bridge vibrates. String players call this playing an open string. When you play an open string, a standing waves is formed, with a node at the nut and another at the bridge. The effective string length equals the distance from nut to bridge.
When you play an open string, the string vibrates in many modes at the same time. The result is a complex sound with a distinct fundamental and many overtones. The overtone frequencies are whole number multiples of the fundamental. String players know that you can change the timbre of the instrument just by changing where you pluck (or bow). Pluck or bow close to the bridge and the sound is harsh- full of higher overtones. Play further from the bridge and the sound becomes more mellow- you get more of the fundamental and lower overtones and less of the higher overtones.
Tuning pegs
The tuning pegs are designed to adjust the pitch of the open string. The pegs work by controlling the tension of the string. Tightening the string increases the speed of waves in the string.
Stop to think 1
What effect does tightening a tuning peg while playing an open string have on wavelengths of standing waves on the string? How does it affect the pitch? Explain your answers, based on the model of the string.
Different strings
Most string instruments have several strings, each with a different composition and/or thickness. On many string instruments like violin and guitar, the strings all have the same length because they share a single bridge and a single nut. Using strings with different density with the same length allows for very different pitches at roughly the same string tension. (Keeping the tension roughly equal across all strings has benefits for the player as well as the instrument).
Stop to think 2
Explain why the heavier strings on a guitar produce lower notes, even if all the strings are strung at the same tension. Use the equation [latex]v=f \lambda[/latex] in your answer.
Fingered notes
To change the note that the instrument makes, the player can press the string firmly against the fingerboard. This shortens the part of the string that vibrates. The effective string length is now from the player’s finger to the bridge. Pressing the string directly down on the fingerboard has virtually no effect on string tension.
Stop to think 3
Compare the open string to a fingered note. What effect does pressing the string firmly against the fingerboard have on each of the following quantities: wavelengths of standing waves, speed of waves on the string, and pitch of the sound?
Harmonics
A string player can also touch the string lightly. This stops the string from vibrating at the finger’s location. Most of the time, this action simply stops the entire string from vibrating. However, if the string is touched lightly in just the right location, a node is formed at the finger’s location and the entire string- from the nut to the finger and from the finger to the bridge- vibrates. String players call this technique harmonics. The sound of a string harmonic is a little spooky- thinner, yet somehow clearer than open strings or fingered string. The guitar’s opening e-minor chord in “Roundabout” by Yes is an example. By lightly touching the strings at the middle, Yes’ guitarist forces a node to form at the middle of the string. The entire string vibrates, but only in modes that that have a node at the middle (n=2, n=4, n=6, etc.)
Stop to think 4
The open A-string of a guitar has a fundamental of 110 Hz. What frequencies will the string produce if the guitarist plucks the string while touching the string lightly 1/3 of the way between the bridge and the nut?
Stop to think answers
- Tightening the tuning peg while playing an open string has no effect on the wavelengths. Wavelengths of standing waves on a string depend only on the length of the part of the string that’s vibrating. Tightening the peg increases string tension, which increases wave speed. When wave speed increases (and wavelength remains unchanged), frequency must increase: [latex]f=\dfrac{v}{ \lambda}[/latex]
- If the tensions are equal, waves travel slower on a heavier string than a light one. When wave speed increases (and wavelength remains unchanged), frequency must increase: [latex]f=\dfrac{v}{ \lambda}[/latex] (The wavelengths are the same for all open strings on a guitar, because the strings are all the same length.
- Fingering a note on a string instrument effectively makes a string that is shorter than the open string, so wavelengths are shortened. Fingering a note has virtually no effect on string tension, so the wave speed is unaffected. The fingered note has a higher frequency than the open string’s note. The reason follows from [latex]f=\dfrac{v}{ \lambda}[/latex], since fingering the note shortens the wavelength but doesn’t affect the wave speed.
- The entire string (from nut to bridge) will vibrate, but only in modes that have a node at the finger’s location. The n=3, n=6, n=9, n=12, etc. modes all have nodes 1/3 of the way from the nut to the bridge, so the sound has a fundamental of 330 Hz and overtones that are whole number multiples of 330 Hz: 660 Hz, 990 Hz, 1320 Hz, etc.
Image credit
Parts of a guitar. Dominic Alves from Wikimedia Commons [1]
- Alves, D. (2010, August 6). Acoustic Guitar. Retrieved from https://commons.wikimedia.org/wiki/File:Acoustic_Guitar_Anatomy.jpg ↵