Exercise 10.5
Graphs representing two sound waves are given in Fig. 10.30. If the scales on the X and Y axes of the two graphs are the same, which of the two sound waves has (i) greater wavelength, and (ii) smaller amplitude? Density
Not cross-checked
NCERT prints no numerical answer for this exercise, so this working has not been cross-checked against the book.
NCERT’s answer
(a)
(ii) (a)
(i) Wave (a) has the greater wavelength. (ii) Wave (a) has the smaller amplitude.
Both graphs plot density against distance on the same scales, so they can be compared square for square.
Wavelength is the distance between two consecutive crests: the crests in (a) are farther apart along the distance axis than those in (b), so \(\displaystyle \lambda_a > \lambda_b \).
Amplitude is the maximum change in density, i.e. the height of a crest above the average-density line: the curve in (a) rises less above that dashed line than the curve in (b), so (a) has the smaller amplitude.
So (a) is the long, gentle wave — lower frequency and less energy — and (b) is the short, tall one that carries more energy and sounds louder.