Fig. 19.1 shows a graph of air pressure variation against distance from a loudspeaker at one instant in time. The graph represents a sound wave travelling t...

Marking Scheme

• (a) [1] Compression
• (b) [1] Rarefaction
• (c) [1] Wavelength = 0.85 m
• (d) [1+1] f = v/wavelength = 340/0.85 = 400 Hz
• (e) [1] A wave with larger amplitude (taller peaks, deeper troughs) but the same wavelength
• (f) [1] A wave with shorter wavelength (more cycles in the same distance) but the same amplitude
• (g) [1] Amplitude (the peak pressure deviation)

Explanation

(a) A compression is the region where air pressure is above normal atmospheric pressure. On the graph, this corresponds to the peaks (maximum positive pressure deviation of +0.4 Pa). In a compression, air molecules are pushed closer together than normal, creating a region of increased density and pressure.

(b) A rarefaction is the region where air pressure is below normal atmospheric pressure. On the graph, this corresponds to the troughs (maximum negative pressure deviation of -0.4 Pa). In a rarefaction, air molecules are spread further apart than normal, creating a region of decreased density and pressure.

(c) The wavelength is the distance for one complete cycle of the wave. From the graph, the distance axis shows markings at 0.85 m intervals. One complete cycle spans from 0 to 0.85 m (or from any point to the corresponding point one cycle later, such as 0.85 m to 1.70 m). Therefore \(\lambda = 0.85\) m. This can also be confirmed by noting that two complete cycles span from 0 to 1.70 m, giving \(\lambda = \frac{1.70}{2} = 0.85\) m.

(d) Using the wave equation \(v = f\lambda\), rearranged: \(f = \frac{v}{\lambda} = \frac{340}{0.85} = 400\) Hz. This frequency is in the audible range and corresponds roughly to the musical note G above middle C. The speed of 340 m/s is given as the speed of sound in the laboratory air.

(e) A louder sound has a greater amplitude. On the pressure-distance graph, this means the peaks would be higher (greater positive deviation) and the troughs deeper (greater negative deviation), but the spacing between peaks (wavelength) stays the same. The wave carries more energy per cycle when the amplitude is larger.

(f) A higher-pitched sound has a greater frequency. Since the graph shows pressure against distance, a higher frequency at the same speed means a shorter wavelength (\(\lambda = \frac{v}{f}\), so increasing \(f\) decreases \(\lambda\)). The sketch would show more complete cycles fitting into the same horizontal distance, with the peaks closer together, but reaching the same height (same amplitude = same loudness).

(g) The loudness of a sound is determined by its amplitude. On this graph, the amplitude is the peak pressure deviation, which is 0.4 Pa. A sound wave with a larger pressure deviation (larger amplitude) carries more energy and is perceived as louder. Frequency determines pitch, not loudness; wavelength determines the spatial extent of each cycle.