Question 18
(a)
State what is meant by the frequency of
a progressive wave. [2]
(b)
A cathode-ray oscilloscope (c.r.o.) is used to determine the
frequency of the sound emitted by a loudspeaker. The trace produced on the
screen of the c.r.o. is shown in Fig. 4.1.
Fig. 4.1
The time-base setting
of the c.r.o. is 250 μs cm-1.
Show that the
frequency of the sound wave is 1600 Hz. [2]
(c)
The loudspeaker in (b) emits the sound in all
directions. A person attaches the loudspeaker to a string and then swings the
loudspeaker at a constant speed in a horizontal circle above his head.
An observer, standing
a large distance away from the loudspeaker, hears sound of maximum frequency
1640 Hz. The speed of sound in air is 330 m s-1.
(i)
Determine the speed of the loudspeaker. [2]
(ii)
Describe and explain, qualitatively, the variation in the frequency
of the sound heard by the observer. [2]
[Total: 8]
Reference: Past Exam Paper – November 2016 Paper 21 & 23 Q4
Solution:
(a)
Frequency
of a progressive wave is the number of oscillations of a point on the wave per
unit time.
(b)
{Starting
from the first peak (crest) on the left,
2
waves occupies 5 cm
1
wave occupies 5/2 = 2.5 cm
Time-base
setting is 250 μs cm-1. That is, each cm represents
250 μs.}
Period T = 2.5 × 250 (μs)
(= 625 μs)
{Frequency = 1 / T
625 μs =
6.25 × 10-4 s}
Frequency = 1 / (6.25 × 10-4) or 1 / (2.5 × 250
× 10-6) = 1600 Hz
(c)
(i)
{Since the source of wave is moving relative to
the observer, Doppler effect occurs.
When the source moves towards the observer
(approaching), the observed wavelength decreases and so, the observed frequency
increases. From the Doppler effect formula, the negative sign is used.
Observed frequency, f0= 1640 Hz
Frequency of source, fs = 1600 Hz (as
calculated above)
Speed of sound, v = 330 m s-1
Speed of source of wave (loudspeaker) = vs
}
For maximum frequency:
fo = fsv / (v – vs)
1640 = (1600 × 330) / (330 – vs)
vs =
8(.0) m s-1 (8.049
m s-1)
(ii)
{Note that as the loudspeaker is moved in
circle, at some point it is moving closer to the observer and at some point, it
is moving further away from the observer.}
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