Question

Show graphically how density of air varies with distance when a periodic sound wave travels in it. Show the graph for two instants of time differing by half of periodic time.

Accepted Answer

The figures given below represent the density and pressure variations of the medium during the propagation of the sound wave. Compressions are regions where particles are crowded together and represented by a level higher than the average. Thus, the peak in the diagrammatic representation shows the maximum value of compression. As a result, the compressions are the region of high density as well as high pressure. Rarefactions are the regions of low density as well as low pressure and are represented by a level lower than the average value. By convention, the peak is called the crest and the valley is called the trough of the wave. The distance between two consecutive crests is called wavelength $(λ)$ .

The crest on the density time graph represent the high density region or compression whereas the trough represents the low density region or rarefaction. In last figure, we can see that at time $t = 0$ , the particle density starts increasing and reaches its maximum value which is represented by crest in graph. Then the density of particles starts decreasing and comes back to average. The density of particles reduces further more and becomes least which is represented by low density region or trough of the graph. Time period is the time taken by a particle of the medium to make one complete vibrational cycle.

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