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Sonometer

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.

Observations

To find the relation between frequency and length

Constant tension on the wire, T= .........kg

Sl No. Frequency of tuning fork used, f (Hz) Resonant length of wire

1/ l

(cm-1)

Length increasing l1(cm)

Length decrasing l2 (cm) 

Mean                 l = (l1 +l2) / 2
           
           
           
           

To find the relation between length and tension

Sl No. Load, M (kg) Tension, T=Mg (N) Resonant length of wire

l 2

(cm2)

l 2 / T

(cm2 / N)

Length increasing l1(cm) Length decrasing l2 (cm) Mean           l = (l1 +l2) / 2
               
               
               
               

                                                                                                     Mean, l2 / T =.................. cm2 / N

Calculations

To find the relation between frequency and length

  • Find mean resonant length, l
  • Calculate 1/l in each case.
  • Plot a graph between frequency and reciprocal of length, taking frequency along X axis and reciprocal length along Y axis.

To find the relation between length and tension

  • Find square of resonant length (l2) each time.
  • Calculate corresponding l2/T value.
  • Plot a graph between square of length and tension, taking tension along X axis and square of length along Y axis.

Results

The frequency V/s reciprocal of length graph is a straight line, which indicates that, frequency is inversely proportional to resonant length.

From the tabular column, it is found that; l2/T is a constant. The graph between square of length and tension is a straight line, which shows that tension is directly proportional to square of resonant length.

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