Two waves of the same pitch have amplitudes in the ratio 1:3. What will be the ratio of their:

(i) loudness

(ii) pitch?

(i) Loudness (L) ∝ [amplitude (a)]²

Ratio of loudness =

$\dfrac{\text{L}$1}{\text{L}2} = \dfrac{(\text{a}1)^2}{(\text{a}2)^2} = \dfrac{(1)^2}{(3)^2} = \dfrac{1}{9}

So L₁ : L₂ = 1 : 9.

(ii) Frequency remains the same if the pitch remains unchanged.

$\dfrac{\text{pitch of 1st wave}}{\text{pitch of 2nd wave}} = \dfrac{\text{1}}{\text{1}} = 1:1$

So pitch will be 1 : 1.