Question 179: [Waves] (Past Exam Paper – November 2008 Paper 1 Q24 & June 2013 Paper 12 Q25)
Diagram shows two waves X and Y.
Wave X has amplitude 8 cm and frequency 100 Hz.
What are the amplitude and frequency of wave Y?
Solution 179:
Answer: D.
Amplitude is the maximum displacement. From the diagram, the amplitude of Y is half that of X. So, amplitude of Y = 8 / 2 = 4cm.
Consider 1 period of X (starting a time = 0) on the diagram. It can be seen that for this amount of time, there are 3 periods of wave Y.
So, the period of wave Y is a third of that of wave X.
Period of wave Y = (1/3) x Period of wave X
Frequency = 1 / Period
Since frequency is inversely proportional to the period, the frequency of wave Y is 3 times that of wave X.
Frequency of wave Y = 3 (100) = 300Hz
OR
For X, period = 1 / 100 = 0.01s.
As seen from diagram, period of Y is one third that of X (in wave Y, 3 oscillations occurs for the same amount of time), so period of Y = 0.01 /3.
Frequency of Y = 1 / [0.01/3] = 300Hz.
(or you could directly obtain the frequency to be 3 times that of X if you understand the concept of frequency well)
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