For the fundamental mode of a sonometer wire, which proportionalities are correct when all other relevant quantities are held fixed?
Select all that apply

Question

For the fundamental mode of a sonometer wire, which proportionalities are correct when all other relevant quantities are held fixed?

G1 Physics · Accepted Answer

The fundamental frequency is f = [1/(2L)]√(T/μ). Hence, f ∝ 1/L, f ∝ √T, f ∝ 1/√μ. For a wire of density ρ and diameter d, μ = ρπd²/4. Thus, √μ ∝ d, so f ∝ 1/d. Therefore all four statements are correct.