CAPE Physics Unit 1 · 2007 · Paper 2 · Question 2

Blowing across a soft-drink bottle creates a tone, a phenomenon called cavity resonance, where the pitch depends on the amount of drink. Scientists have derived a formula for the frequency produced: f = (c / (2π)) * √(A / (LV)), where c is the velocity of sound in the cavity, A is the area of the neck, L is the length of the neck, and V is the volume of air. An experiment used a small speaker and signal generator to find resonant frequencies for various air volumes. The bottle had a neck length of 5.9 x 10⁻² m and a cross-sectional area of 2.55 x 10⁻⁴ m².

When you blow across the top of a soft-drink bottle as shown in Figure 2, a tone is heard. The pitch of the sound depends on how much drink is left in the bottle. This phenomenon is called cavity resonance. Scientists investigating cavity resonance have deduced a formula for the frequency produced: f = (c / (2π)) * √(A / (LV)) where c = velocity of sound in the cavity, A = area of the neck of the bottle, L = length of the neck of the bottle, V = volume of air in the cavity. Using a small speaker connected to a signal generator the resonant frequency may be found for various values of the air volume. The data obtained from one such experiment are shown in Table 1. The bottle used had a neck length of 5.9 x 10⁻² m and the cross-sectional area of the neck was 2.55 x 10⁻⁴ m².

This question uses a figure or table from the paper — you'll see it when you practise.