algebra question

Question

The frequency of a vibrating string is inversely proportional to its diameter. A violin string with diameter 0.50 mm produces a tone of frequency 440 Hz. What is the frequency of the tone produced by a similar string that is 0.05 mm larger?

Answer 1

If 2 variables are inversely proportional they satisfy an equation of the form y = k / x.

So let d be the diameter and f be the frequency, then d = k / f.

Plug in the given values of d and f to find k, then use the equation to find f at the new diameter.

Answer 2

The relation for inverse proportionality is

d₁f₁ = d₂f₂ ⇒

f₂ = d₁f₁ / d₂

d2 = (0.50 + 0.05) mm = 0.55 mm

f₂ = d₁f₁ / d₂ = (0.50 mm)(440 Hz) / (0.55 mm) = 400 Hz