Question 8
An arrangement for
producing stationary waves in air in a tube that is closed at one end is shown in
Fig. 6.1.
Fig. 6.1
A loudspeaker produces
sound waves of wavelength 0.680 m in the tube.
For some values of the
length L of the tube,
stationary waves are formed.
(a)
Explain how stationary waves are formed in the tube. [2]
(b)
The length L is adjusted between
0.200 m and 1.00 m.
(i)
Calculate two values of L for which stationary
waves are formed. [2]
(ii)
On Fig. 6.2, label the positions of the antinodes with an A
and the nodes with an N for the least value of
L for which a stationary wave is formed.
Fig. 6.2
[1]
Reference: Past Exam Paper – November 2015 Paper 23 Q6
Solution:
(a)
Waves from
the loudspeaker travel down the tube and are reflected at the closed end. This
produces wave travelling in opposite directions to the waves from the loudspeaker
but with the same frequency. When these two waves overlap, stationary waves are
formed.
(b)
(i)
0.51 m
0.85 m
{For a tube
closed at one end, the stationary waves formed are as follows:
Fundamental
mo
de: λ = 4L giving L = λ/4 = 0.680 / 4 = 0.17 m (not
in range)
1st
overtone: λ = 4L/3 giving L = 3λ/4 = 3×0.680 / 4 = 0.51 m
2nd
overtone: λ = 4L/5 giving L = 5λ/4 = 5×0.680 / 4 = 0.85 m}
(ii)
A at open
end, N at closed end, with an N and A in between, equally spaced
(by eye)
thank you so much may allah bless you
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