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Theory & Procedure, Sonometer Notes | Study Additional Documents & Tests for NEET - NEET

Document Description: Theory & Procedure, Sonometer for NEET 2022 is part of Additional Documents & Tests for NEET preparation. The notes and questions for Theory & Procedure, Sonometer have been prepared according to the NEET exam syllabus. Information about Theory & Procedure, Sonometer covers topics like and Theory & Procedure, Sonometer Example, for NEET 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Theory & Procedure, Sonometer.

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Objective

  • To study the relation between frequency and length of a given wire under constant tension using sonometer. To plot a graph between ν and l.
  • To study the relation between length of a given wire and tension for constant frequency using sonometer. To plot a graph between l2 and T.

Theory

What is a Sonometer?

Sonometer consists of a hollow rectangular wooden box of more than one meter length, with a hook at one end and a pulley at the other end. One end of a string is fixed at the hook and the other end passes over the pulley. A weight hanger is attached to the free end of the string. Two adjustable wooden bridges are put over the board, so that the length of string can be adjusted.

Theory & Procedure, Sonometer Notes | Study Additional Documents & Tests for NEET - NEET

Production of transverse waves in stretched strings

If a string which is stretched between two fixed points is plucked at its center, vibrations produced and it move out in opposite directions along the string. Because of this, a transverse wave travels along the string.

If a string of length l having mass per unit length m is stretched with a tension T, the fundamental frequency of vibration f is given by;

Theory & Procedure, Sonometer Notes | Study Additional Documents & Tests for NEET - NEET

Laws of transverse vibrations on a stretched string

  • Law of Length: The frequency of vibration of a stretched string varies inversely as its resonating length (provided its mass per unit length and tension remain constant.)
    Theory & Procedure, Sonometer Notes | Study Additional Documents & Tests for NEET - NEET
  • Law of Tension:The frequency of vibration of a stretched string varies directly as the square root of its tension, (provided its resonating length and mass per unit length of the wire remains constant).

Theory & Procedure, Sonometer Notes | Study Additional Documents & Tests for NEET - NEET

Relation between frequency and length

From the law of length,  f ×l = constant

A graph between f and 1/l will be a straight line.

Relation between length and tension

From the equation for frequency, √T / l = constant

A graph between T and l2 will be a straight line.

Learning outcomes

  • Students develop the idea about standing waves.
  • Students understand the sonometer apparatus and its working.
  • Students get the relation between frequency, length and tension of a stretched string under vibration.

Materials Required

  • A sonometer
  • A set of tuning forks of known frequency
  • 0.5kg weight hanger
  • Some 0.5kg slotted weights
  • Rubber pad
  • Paper rider

Real Lab Procedure

To find the relation between frequency and length

  • Place the sonometer on the table.
  • Make sure that the pulley is frictionless. If you feel any friction, oil them.
  • Stretch the wire by placing a suitable maximum load on the weight hanger.
  • Move the wooden bridges outward, so that the length of wire between the bridges is maximum.
  • Take a tuning fork of known frequency. Make it vibrate by strike its prong with a rubber pad. Bring it near the ear.
  • Pluck the sonometer wire and leave it to vibrate. 
  • Compare the sounds produced by tuning fork and sonometer wire. (Sound which has low pitch has less frequency).
  • Gently adjust the bridges for decreasing the length of wire, till the two sounds appear alike.
  • Put an inverted V shaped paper rider on the middle of the wire.
  • Vibrate the tuning fork and touch the lower end of its handle with sonometer board. The wire vibrates due to resonance and the paper rider falls.
  • Measure the length of wire between the bridges using a meter scale. It is the resonant length and record it in the ‘length decreasing’ column.
  • Now, bring the bridges closer and then slowly increase the length of the wire till the paper rider falls.
  • Measure the length of wire and record it in ‘length increasing’ column.
  • Repeat the above steps with tuning forks of other frequencies, and find resonant length each time.

To find the relation between length and tension

  • Select a tuning fork of known frequency
  • Set the load in the weight hanger as maximum.
  • Repeat the steps in the previous section to find out the resonant length.
  • Now, remove 0.5kg weight from the weight hanger and find resonant length with same tuning fork.
  • Repeat the experiment by removing slotted weights one by one in equal steps of 0.5kg.
  • Record the observations each time.

Simulator Procedure (as performed through the Online Labs)

  • Select the environment from the drop down list.
  • Select the material of the wire from the drop down list.
  • Select the diameter of the wire using the slider.
  • Select the weight of the slotted weights using the slider.
  • Select the frequency of the tuning fork using the slider.
  • Click on the ‘Hit tuning fork’ button to start/stop the vibration of tuning fork and touch it with the sonometer board.
  • Change the position of bridge A using the slider.
  • Change the position of bridge B using the slider.
  • Click on the ‘Place the paper rider’ button to place the paper rider back.
  • To redo the experiment, click on the ‘Reset’ button.
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