Talking About Strings: The Physics of Tone and Tension

By Ian Weston, Topaz & Weston Instruments

1. Quality and Consistency

Not all strings are created equal. In my workshop, we recommend a narrow selection of brands known for their metallurgical consistency and reliability: D'Addario is by far the best. Good results can also be achieved with Elixir, Ernie Ball, and GHS. For Bass: D’Addario, Ernie Ball, Smith and LaBella.

The "Handmade" Myth: While "handmade" sounds prestigious, string manufacturing requires extreme mechanical precision. Lower-quality strings have inconsistent vibration patterns, causing buzzing and poor intonation. Avoid handmade strings; they are rarely precise enough to intonate correctly.

2. Hooke’s Law: The Physics of Guitar Strings

To understand why heavy gauge strings occupy less space when vibrating, we look to Hooke’s Law of Elasticity. This law states that the extension of a spring is in direct proportion to the load applied to it.

The Formula:

Mathematically, Hooke’s Law is expressed as:

F = k * x

Where:

• F is the restoring force exerted (Tension).

• k is the spring constant (the stiffness of the string).

• x is the displacement (the "pluck" or distance from equilibrium).

The Comparison: .010 vs .011

To prove that heavier strings have a smaller amplitude (xp) under the same plucking force (Fp), we calculate the spring constant (k) using Young’s Modulus (E) for nickel (200 GPa) and the cross-section area (A) of the string:

k = (E * A) / L

• 0.010" String Area (A1): 0.051 mm2

• 0.011" String Area (A2): 0.061 mm2

The Result:

Since xp = Fp / k, and our plucking force (Fp) is constant, we find that:

xp1 > xp2

Scientific Conclusion: Because the .011 string has a higher spring constant (k), it stretches less under the same force. The amplitude of its standing wave is smaller, meaning it requires less clearance over the frets to vibrate cleanly.

3. Performance Factors

• Output: Heavier strings possess more stored energy. On an electric guitar, the thicker mass incurs a stronger variation in the magnetic field of the pickups, resulting in a hotter, fuller signal.

• Artificial Harmonics: Producing pinch harmonics is significantly easier on heavier strings because of the increased tension and stored energy. A slack string (like a light gauge tuned down) makes it difficult to cancel out the fundamental tone.

• Intonation: All strings stretch when brought to pitch, but their vibration also stretches them. Heavier gauges resist this "vibrational stretching," leading to more stable pitch during aggressive playing.

• Sustain: Because heavier strings have more stored energy, they have more energy available for release over time.

• Picking Speed: While heavier strings require more finger strength, they offer more "push back" against the pick. Because the strings move less, skipping between strings is swifter and easier to control.