A diddley bow is one string stretched between two bridges over a board and played with a slide, and the string must be strong enough for its pitch: a 0.5 mm steel wire over 0.80 m tuned to 110 Hz carries 47.7 N, which is 243 MPa of stress. The stress depends only on the wire’s density, its length and the pitch, not on its thickness, so a thinner wire does not make a higher note safer. Never tune a salvaged wire up to a pitch you have not tested it for.
Part of Music & Simple Instrument Making
The simplest stringed instrument: tension, stress and fret positions worked out from the string equation.
The Equation Behind The Board
A string of length L, tension T and mass per metre μ vibrates at f = (1 ÷ 2L) × √(T ÷ μ). Its wave speed is v = √(T ÷ μ) = 2Lf. Because μ = ρ × A (density times cross-section) and stress is σ = T ÷ A, then v² = σ ÷ ρ, so
σ = ρ × (2Lf)²
The stress needed to reach a pitch depends only on the material’s density, the string length and the frequency. Thickness cancels out: a thicker wire carries more force but at the same stress.
Worked Example: A Steel Wire At 110 Hz
Inputs: wire diameter d = 0.5 mm = 0.0005 m, speaking length L = 0.80 m, target f = 110 Hz (A2, two octaves below the A of 440 Hz), and a steel density I recalled as 7,850 kg/m³ (a standard handbook value; salvaged wire may differ).
- Cross-section: A = π × d² ÷ 4 = π × (0.0005)² ÷ 4 = 1.963 × 10⁻⁷ m²
- Mass per metre: μ = ρ × A = 7,850 × 1.963 × 10⁻⁷ = 1.541 × 10⁻³ kg/m
- Wave speed: v = 2Lf = 2 × 0.80 × 110 = 176 m/s
- Tension: T = μ × v² = 1.541 × 10⁻³ × 176² = 1.541 × 10⁻³ × 30,976 = 47.7 N, which is 47.7 ÷ 9.81 = 4.9 kg hanging
- Stress: σ = T ÷ A = 47.7 ÷ 1.963 × 10⁻⁷ = 2.43 × 10⁸ Pa = 243 MPa (check: ρ × v² = 7,850 × 30,976 = 243 MPa)
The same wire at the same length:
| Pitch | Wave speed (m/s) | Tension (N) | Stress (MPa) |
|---|---|---|---|
| 55 Hz | 88 | 11.9 | 61 |
| 110 Hz | 176 | 47.7 | 243 |
| 220 Hz | 352 | 191.0 | 973 |
Doubling the pitch quadruples tension and stress. At 220 Hz the stress, 973 MPa, may exceed what soft iron or mild-steel wire can bear. I could not source a strength figure for salvaged wire, so test it: see String Materials for a break test. Music-type steel wire is made far stronger than soft wire; fence wire is not.
Fret Positions For A Slide
A bottleneck slide stops the string at distance x from the nut. For n semitones above the open note, the remaining length is L ÷ 2^(n/12), so x = L × (1 − 2^(−n/12)). For L = 800 mm:
| Semitones | Position from nut (mm) |
|---|---|
| 1 | 44.9 |
| 2 | 87.3 |
| 3 | 127.3 |
| 4 | 165.0 |
| 5 | 200.7 |
| 7 | 266.1 |
| 12 | 400.0 |
The octave sits at exactly half the string, 400 mm, and the spacing shrinks as you go up. The same table makes a pitch reference for tuning flutes; see Hole Spacing & Tuning.
What You Need
- A board, 60-100 cm long, as the parent article specifies, stiff enough not to bow under 47.7 N
- Two pegs or nails at the ends to anchor the wire (a tuning peg at one end helps)
- Wire — salvaged steel wire, or a sheet-metal strip; see Iron Wire
- Two small bridges (wood or bone) to lift the string above the board
- A resonator — a gourd, box or pot under the board
- A slide — a smooth stone, bone or bottle neck
Method: Build, Test, Play
Step 1: Drive the end pegs into the board’s ends; use hardwood or fix with lashings so they do not pull out under the string’s tension.
Step 2: Fit the bridges a few centimetres in from each end and a finger-width above the board; the speaking length L is the distance between them.
Step 3: Tie the wire, raise it gradually to tension, and stop at the target pitch or earlier if the board bends.
Step 4: Mount over a resonator so the sound is audible.
Step 5: Play with a slide that touches the string lightly and does not press it to the board; the slide’s position sets the pitch.
Common Mistakes
- Using cord. A cord or twine will not give a clear sustained pitch; use wire or a stiff string.
- Pegs that pull out. A nail driven into end grain slides out under 47.7 N; use a hardwood block or lash it.
- Bridges too high. The string goes sharp when you press it; keep them low.
Safety
A wire under tension can snap and whip
Wear eye protection when tuning. At 47.7 N the stored energy is small but a thin wire can still cut or strike an eye. Tune slowly, keep your face out of line with the wire, and do not tune beyond a pitch the wire has been tested for. File off sharp wire ends and cap them.
What’s Next
- Learn next: Simple Lyre (3-5 strings) — several strings on a frame
- Combine with: String Materials — choosing and testing the string