NCERT Solutions for Class 9th Science Chapter 10 .5 Graphical Representation of a Sound Wave — Pause and Ponder
Book page 19310 Updated on2026-09-19
Q1.
The variation of density of the medium for two sound waves is shown in Fig. 10.17 (a) and (b). Label compression and rarefaction by C and R on it. In the graph given in Fig. 10.17 (c) and (d), label the axes and draw the curves corresponding to Fig. 10.17 (a) and (b).
Fig. 10.17, page 193. (a) and (b) show the density of the medium for two sound waves; (c) and (d) are the empty graph grids to be labelled and filled in.
Answer
Labelling (a) and (b). Wherever the dots are crowded together the density is above average — mark that C. Wherever the dots are thinned out the density is below average — mark that R. In the printed figure, guide lines are drawn through the centres of these regions.
In (a) the first dashed guide line — the one at the left-hand edge — runs through a dense band, so mark C there, R at the next dashed line, and C and R alternately at every dashed line after that. The solid lines midway between them mark the places where the density is exactly average.
In (b) the guide lines stand in exactly the same places, but the dot pattern is shifted by half a wavelength: the first dashed line now runs through a thinned-out band, so it is R there and C at the next dashed line. A place that is a compression in (a) is a rarefaction in (b). Both strips have the same wavelength.
Labelling the axes of (c) and (d). Along the horizontal axis write Distance; along the vertical axis write Density; and draw a horizontal dashed line for the average density.
Drawing the curves. Every C becomes a crest (maximum density) and every R becomes a trough (minimum density). So:
(c), matching (a): the curve starts at a crest above the average-density line, at the first dashed guide line on the vertical axis.
(d), matching (b): the same curve shifted by half a wavelength — it starts at a trough where (c) had a crest.
Top: the dot pattern of (a) with C and R marked, and below it the matching density–distance graph (c) — a crest at every C, a trough at every R. Bottom: graph (d) for strip (b), the same wave shifted by half a wavelength.
Why the graph looks like a smooth wave when the picture is only dots: the graph does not plot particles — it plots the density of the medium at each distance, at one instant. Density rises smoothly to a maximum in the middle of a compression and falls smoothly to a minimum in the middle of a rarefaction, so the plot comes out as a smooth curve about the average-density line.
Tip: keep the vocabulary straight — crest is the highest point of the graph (maximum density, i.e. a compression), trough is the lowest point (minimum density, i.e. a rarefaction). A sound wave is longitudinal even though its graph looks like a wiggle.