育教儒堂其三第張六第
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1973英文中學會考試題預習專欄
For the first harmonic, we can see that
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Using
物理科
(廿九)
三期星
日九月五年三七九一番公年二十六闖民輩中
or L+ C
Organ pipes are similar to reson-
ance tubes. The air column vibrat -ing in ita fundamental mode in an open pipe is given in fig 9 whereas in fig 10 is the fundament -al mode in a closed organ pipe.
K-30-*
1st maduum and
mad
The angle of refraction, r, can calculated by using the Smell'e law.
N
A
sin
sin
Applying
angle of
incidence
Physics (29)
Determination of the frequency
of the a.c. mains.
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The ac mains is connected across the bridges of a sonometer. The poles of a horse-shoe magnet is placed across the mid-point of the wire to amplify the amplitude of vibration of the string. By switching on the mains and adjust- ing the position of the bridges, a position can be reached at which the length of the wire stretched between the bridges is in unison with the a.c. mains. This can be indicated by placing a small V-shaped paper across the wire so that when resonance be tween the wire and the a.c. mains occurs, the paper rider falls off the wire, The length of the wire between the bridges is measured. The tension in the string and the masa perunt length of the string can also be determined. Applying
The frequency of the a.c. mains, f, can be determined.
2. Determination of frequency of an unknown tuning fork,
The tuning fork whose fre- quency is required is struck on a plastic pad and held near the sonometer wire on which a paper rider is placed. The vibrating length of the string is adjusted until the wire stretched across the bridges is in unison with the tuning fork. The length of the wire between the bridges is noted. The experiment is repeat- ed with a standard tuning fork, ie one whose frequency is known The vibrating length is again measured. Using
For the second harmon
2V
For the third harmonic,
L
general, for the nth harmonic
If the glass tube is closed at one end, the open end is always the end at which an antinode. »!! present and the close end, a node present. The fundamental mode is that mode which is 2 of a complete loop
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The second harmonic is absent. The third harmonic consists of tw antinodes and two nodes as shown in fig. 6.
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The fourth harmonic is absent. The fifth harmonic or the third overtone is shown in fig 7.
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In general, a half open glass tube has only odd harmonies. All the even harmonics are absent. For the fundamental mode,
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For the third harmonic,
Determination of the velocity of sound in air.
An open glass tube is mounted vertically on a stand. The lower end of the tube is connected to a reservoir containing water by. means of a rubber tubing.
nuthern tubing
The water level in the tube can be changed by raising or lowering the reservoir. A tuning fork of known frequency is sounded near the open end of the tube when the water level is at its highest position. By raising the reservo- ir, the air column inside the tube increases in length. A position can be reached at which a sudden intense sound is heard. The air column is now in unison with the tuning fork. The mode of vibrat ior is that of the fundamental.
k/27:3 20:
500 = 1273
5.00/1 +
518.3 m/s..
Since both hydrogen and air are diatomic, they have the same value of
Applying V
For air 331
For hy
76
10.0396
Where V is the velocity of sound in hydrogen at 0°C,
By division, V331
Appl
1257 m
k/273
/293
velocity of sound hydrogen at 2000
V' = 1257
1293
273
1300 m/8*
Since V
(a) 480
160.
160
(2)
0.5 m
Hence
(b) £2
2. X
480 x 0.6 = 288 hz.
(80
III
Where is the length of the air colum and C is the end correction
480 x (7)2
18.00
(c),
-(4)
程
-(2 X 12 > Ty).
2
Ly + C = 27
The experiment is repeated to obtain the second overtone when the length is 12.
Hence
we get I'l
where
the unmown frequency, &, its resonance length and 11⁄2 is the frequency of the standard fork and its resonance length.
Hence
is found.
Vibrating air columns
Stationary waves (ie. superposit- ion of waves travelling in oppos- ite directions) can also be set up in a long glass tube. If the glass tube is opened at both ends, the simplest mode of vibration is that of a wave of two antinodes at the open enda and a node at the mid-point of the tube.
This is the fundamental mode or the first harmonic. The second harmonic or the first overtone is the mode of vibration in which the antinodes are at the open ends and at the mid-point of the tube, the nodes at the points 1/4 and 3/4 of the length of the tube from an open end.
The third harmonic or the second. overtone is the mode shown in fig 4.
X 4731
=
5V
For the fifth harmonic,
In general, for the nth harmonic where n is odd.
In the above treatment, the open ends of the tube are taken as the positions at which the antinodes are located. This is not true. The antinodes are at a small distance above (& below) the open ends. This small distance is called the end correction C.
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Thus for open tubes, the fundament -al mode has ita wavelength given by
There
L20
社
21(1 +20)
or L+ 20 = 21
Similar equations can be obtained for higher harmonics.
For half-open tubes, the waveleng th becomes
?=
=I+C.
For the fundamental node.
V = 4f (L+ C)
21 (D2- I1)
The velocity of sound in air at the room temperature is determined Substituting the value of C in (1) or (2), the end correction can be found. If a number of standard tuning forks are avail- able, the experiment can be re peated for each tuning fork with the air colum vibrating in its fundamental mode. A graph of I plotted against is a straight line is – and the intercept on the L-axis is the (negative of the) er end correction C.
5. Beata.
7
When two tuning forks of near ly the same frequency are sounded near to each other, a periodic fall and rise in sound intensity is heard. This phenomenon is called the beat. The beat fre- quency is equal to the difference between the two Frequencies.
Solution to exercise' 8.
(a) Distance between successive crests - wavelength - 30 or
Wave velocity
42
The frequency =
21 cm/sec.
30 = 0.7 az
(b) Refractive index of the
second medium
wave velocity in the first medium
wave velocity in the second medium
21
The frequency of the wave is unchanged in going from one mediur to another, The wavelength become -8 14 20 cm. Hence the wave-
length decreased in the second medium. The waveform is as shown in fig 12.
480 x 0.6 x
= 204 hz.
Since 8 segments are formed in 420 cm length of the string, the wavelength of the wave is
420
105 cm. The mode of
vibration is that of the 8th harmonic
oplying
Exercise 9.
180x420
2 x 420
72 hz.
The wire of a sonometer 1 long weigha 5 gm and is stretch -ed by a force of 10 kgt When the length of the vibrating portion of the wire is 28 cm; 3 boats, per second are heard if the wire and a fork of unknown frequency are sounded together. The wire is slightly shortened and 4 beate per second are then heari. What is the frequency of the fork?
A narrow test-tube, 15 om. long emita a note of frequency 563 hz when a current of air is blown across its mouth, the temperature being 1000. Determine the velocity of sound at 0°0.
3. Find the length of an organ
pipe open at both ends that .... will give a fundamental note, of frequency 256 hz in air at 2000, the total end correction being 4.5 cm. (velocity of sound in air at 0°0 = 331 m/s). 4. A sonometer wire of length
76 cm, is maintained, und er a tension of 4 kgf and an a.c. is passed through the wire. horse-shoe magnet. is placed with its poles above and below the wire, at its mid-point, and the resulting force get the wire in resonant vibration. If the density of the material of the wire is, 8.8 gm/co. and the diameter of the wire is 1 mm., what is the frequency of the a.c. mains?