How to solve questions on wave motion
Question 1
Given the progressive wave equation{UTME 2008}
calculate the wavelength.
A. 12.4m B. 15.7m C. 17.5m D. 18.6m
Solution
using the wave equation
compare this wave equation with the one given in the question
K is the phase difference
B is the correct option
Question 2
If a light wave has a wavelength of 500nm in air, what is the frequency of the wave?{UTME 2009}
A. 3.0 x 1014 Hz B. 6.0 x 1014 Hz C. 6.0 x 1012 Hz D. 2.5 x 1014 Hz
[c = 3 x 10^8 ms-1]
v = fℷ
nanometer = 10^-9 m
3 x 10^8 = f x 500 x 10^-9
f = 3 x 10^8 / 500 x 10^-9
f = 6.0 x 10^14 Hz
B is the correct option
Question 3
The wavelength of a wave travelling with a velocity of 420ms-1 is 42 m. What is its
period?{UTME 2010}
A. 1.0s B. 0.1s C. 0.5s D. 1.2s
Solution
v = ℷ / T
T = ℷ / v
T = 42 / 420
T = 0.1 s
B is the correct option
Question 4
A microphone connected to the Y-plates of a cathode-ray oscilloscope (c.r.o.) is placed in front of a loudspeaker. The trace on the screen of the c.r.o. is shown below{Cambridge may/june 2016 p12}
The time-base setting is 0.5 ms cm–1 and the Y-plate sensitivity is 0.2 mV cm–1. What is the frequency of the sound from the loudspeaker and what is the amplitude of the trace on the c.r.o.?{ Cambridge may/june 2016 p12}
Solution
The y-sensitivity will measure the amplitide which is on the y-axis
The time-base setting will measure the period which is on the x-axis
From the graph representation a full cycle occupies 6boxes
and one box to the x-axis o.5ms
period (T) = no of boxes x value of one box(which is 0.5 ms)
T = 6 X o.5 = 3 ms
Frequency(f) = 1 /T
f = 1 / (3 x 10^-3) = 333 Hz = 330 Hz approximately
from the graph the amplitude occupies 3 boxes i.e. maximum displacement from the rest position
and one box to the y-axis o.2 mv
A mplitude = no of boxes x no of one box(which is 0.2mv)
A = 3 x 0.2mv
A = 0.6 mv
A is the correct option
Question 5
The variation with time t of the displacement y of a wave X, as it passes a point P, is shown in
use the diagram to determine the frequency of wave X.{ Cambridge may/june 2016 p12}
from the graph the period is 4.0 ms
f = 1 / T
f = 1 / (4 x 10^-3)
f = 250 Hz
Recommended: Click here to read short note on wave motion
