Question

Instruments such as guitars and violins use stretched strings. The tone produced depends on the frequency of a string’s vibration – a higher frequency means a higher tone. Explain why notes of higher tone are produced when fingers are placed on the strings, and why strings for lower tones are thicker or heavier than those for higher tones

Answer 1

For a given string, the wave velocity is set.

Placing a finger on a string changes the effective length of the string and L = nλ/2.

If L is shortened, then so is the resonant wavelength. Since v = fλ, if λ gets smaller, then f must get bigger and vice versa.

Thicker strings have higher linear mass density $\mu$ .

which is related to velocity and therefore frequency as 1/ √µ ∝ v ∝ f, so the greater µ, the smaller f.