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| Sonometer |
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| A sonometer, also called a monochord, was invented by Pythagoras (580-500 B.C.). It is a simple instrument used to verify the laws of stretched strings and to determine the frequency of a tuning fork. It consists of a long hollow rectangular wooden box (w) called the sound box, having three openings on one of its sides. A metal hook or a peg P1, is rigidly fixed at one end with a frictionless pulley P2, attached to the other end. One end of a long metal wire of uniform cross-section tied firmly to the peg, passes over two wedge shaped bridges A and B and then over the pulley. The wire can be stretched by adding suitable load to the weight hanger H which is attached to the other end. C is a movable bridge whose position can be adjusted between A and B so that any desired length of the wire can be set into vibration. |
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| Experiment to determine the frequency of a tuning fork using a sonometer (absolute method) |
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| The weight w1 of the weight hanger H is noted. A load of, say w2 = 1kg is added to the hanger. Now, the tension in the string will be T = (w1 + w2) g
newtons, where g is the acceleration due to gravity. The given tuning fork is struck on a hard rubber pad and the shank of the fork is pressed on the sound box of the sonometer. The vibrations will be conveyed to the air in the box and a fairly loud sound is heard. Now the wire between the bridges A and C is plucked. It vibrates with a frequency which depends on the length AC. |
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| The bridge C is moved to a suitable position till the note of the string matches with that of the tuning fork. When the frequencies are nearly equal, beats will be heard, i.e., there will be waxing and waning of sound intensity. A small movement of the bridge C will cause the beats to stop. In this position, the length AC of the wire will be in resonance with the tuning fork. The resonance can be checked by placing a small inverted V-shaped paper rider on the middle portion of AC. When it is at rest, on placing the vibrating tuning fork on the sound box, the paper rider is found to vibrate vigorously and may be thrown off. The resonating length AC = L is measured using a metre scale. |
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The experiment is repeated by gradually increasing the load W2 in steps of 1Kgwt. The readings are tabulated. It will be found
that  is a constant within the limits of the
experimental error. The mean value of is calculated.
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| A known length of the same kind of wire as used in the sonometer, is weighed accurately in a physical balance to find its mass. Thus, the mass per unit length (m) expressed in Kgm-1 is calculated. The frequency of the tuning fork is then given by the expression |
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| The readings are entered as follows. |
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| Length of the specimen wire = ……m |
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| Mass of the specimen wire = ………. Kg |
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| Mass of the weight hanger = W1 = ........... Kg |
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| The frequency of the given tuning fork = f = ....... Hz |
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| A string can be made to vibrate in different modes. When it vibrates as a whole with two nodes at the extremities and an antinode in the middle, it is the simplest or the fundamental mode of vibration. The frequency is then called fundamental frequency or the first harmonic and it is given by the equation |
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| If a string vibrating in the fundamental mode is gently touched at the
center, a node is formed at that point and the frequency of vibration becomes twice that of the fundamental mode. If the string is touched lightly at a point one third the distance from the end, it will vibrate in three segments and have a frequency three times that of the fundamental mode. The different modes of vibration are shown in figure. |
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| A string can be set into vibrations with its fundamental and several of its higher modes at the same time. This is accomplished by plucking or bowing the string vigorously. The figure shows a string vibrating with two modes at the same time. |
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