The diagram below shows the volume of a small slice of a medium carrying a wave
(longitudinal or transverse included).
What is the total amount of energy carried by a wave
of speed v travelling through S, the
cross-sectional surface area in a certain time t?
E
= 2p2mf2A2
where E is the energy of the wave, m the mass of a particle in the medium,
f the frequency of the wave & A the amplitude of the wave motion.
The energy transported by a wave can also be expressed
by:
E
= 2p2rSvtf2A2
where r is the density of the medium, S the cross-sectional surface area through which the
wave travels, v the speed of the wave, & t
the time taken for the wave to travel the
distance l.
Example 1: A wave propagates from left to right with a
speed of 3.0 ms-1 through a medium of density 1.4 kg m-3.
Given that the frequency of the wave is 8.0 Hz. & the amplitude 60 cm. Determine
the total wave energy that passes through a cross-sectional surface area of 5.0
m2 during a time interval of 40 s.
Answer: E
= 2p2rSvtf2A2
= 2 x 3.142 x 1.4 x 5.0 x 3.0 x 40 x 8.02 x 0.62
= 380,000 J (2 significant figures)
Example 2: The diagram below shows the graphical
representation of 3 waves P, Q & R passing through the same medium during the same period of time.
(i) Compare wave P & wave Q. Which one possesses more energy?
(ii) Compare wave P & wave R. Which one possesses more energy?
Answer:
(i) Frequency of wave Q is 1.5 times that of wave P
(3 Hz ¸ 2 Hz).
There is factor of f2 in the
wave energy equation.
Therefore, wave Q possesses more energy than wave P by a factor of 1.52 or 2.25.
(ii) Amplitude of wave R is 2 times that of wave P.
There is factor of A2 in the
wave energy equation.
Therefore, wave R possesses more energy than wave P by a factor of 22 or 4.
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