A displacement-time graph is shown for a particular wave. A second wave of similar type has twice the intensity and half the frequency.

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.