Question 21
A displacement-time
graph is shown for a particular wave.
A second wave of similar
type has twice the intensity and half the frequency.
When drawn on the same axes, what would the second wave look like?
Reference: Past Exam Paper – June 2006 Paper 1 Q24
Solution:
Answer:
B.
The original graph
contains 2 complete waves on the axes. If the frequency is halved, only 1
period will be displayed on the same axis. [C and D are incorrect]
Changing the frequency
will affect the period of the wave. The frequency does not affect the intensity.
Intensity depends on the amplitude of the wave.
Intensity, I is
proportional to (amplitude, A)2. So, the amplitude is proportional
to √I.
If the intensity is
doubled, the new amplitude becomes √(2I) = √2 √I. So, the new amplitude is
greater by a factor of √2 (≈1.4) than the original amplitude. [A is incorrect]
It is incorrect to assume that twice the intensity of a wave would be the result of twice the amplitude as the intensity is proportional to the square root of the amplitude, not proportional to the amplitude itself.
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