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The ratio of the intensities of two waves is 9:1. The ratio of their amplitudes is

Asked in GUJCET 2008 · Intensity and coherent sources

• (1) 3:1
• (2) 2:1
• (3) 9:1
• (4) 1:9

Step-by-step solution

Why the other options are wrong

• (2) 2:1 would follow from an intensity ratio of 4:1, since I∝ A². For 9:1 the amplitudes are in the ratio √9:√1.
• (3) Treats intensity as proportional to the amplitude. It goes as the square of the amplitude, so the ratio has to be square-rooted, not carried over unchanged.
• (4) Inverts the ratio as well, as though the amplitude fell when the intensity rose.

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