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To determine the frequency of alternating current (A.C.) mains using a Sonometer.

The sonometer is an apparatus used to study the transverse vibrations of stretched strings. In this experiment, an alternating current is passed through a non-magnetic wire stretched over the sonometer box. A strong magnetic field is applied perpendicular to the wire using a horseshoe magnet. The interaction between the oscillating current and the magnetic field causes the wire to vibrate. By adjusting the vibrating length, the natural frequency of the wire is made equal to the frequency of the A.C. source, resulting in resonance.

o study the resonance phenomenon in a stretched string.

To determine the frequency of the A.C. mains supply (Standard is usually 50 Hz or 60 Hz depending on the region).

To verify the relationship between the length of the vibrating segment and the tension applied.

Sonometer: A hollow wooden box with a stretched wire.Step-down Transformer: To lower the 220V mains voltage to a safe 6V.Horseshoe Magnet: To provide a strong, uniform magnetic field.Sonometer Wire: Non-magnetic metallic wire (usually Copper or Brass).Weight Hanger and Slotted Weights: To apply tension ($T$) to the wire.Two sharp-edged wedges (Bridges): To define the vibrating length.Paper Rider: A small V-shaped piece of paper to detect resonance.Meter Scale: To measure the length.

Step 1: SetupPlace the sonometer on a table. Ensure the pulley is frictionless.Connect the step-down transformer (6V output) to the two ends of the sonometer wire.Suspend a specific mass (e.g., $M = 500\text{ g}$) from the free end of the wire using the hanger.Step 2: PositioningPlace the horseshoe magnet at the center of the wire such that the magnetic field is horizontal and perpendicular to the length of the wire.Place the two wooden bridges on either side of the magnet.Step 3: Finding ResonanceSwitch on the A.C. supply. The wire will begin to vibrate slightly.Place a small, light paper rider (V-shaped paper) on the wire in the middle of the two bridges.Slowly adjust the distance between the two bridges by moving them symmetrically outwards or inwards.Watch the paper rider carefully. At a specific length, the wire will vibrate with maximum amplitude (Resonance), causing the paper rider to fly off.Step 4: MeasurementSwitch off the current immediately after the rider falls to stop the vibration.Measure the distance between the two bridges using a meter scale. Record this as the resonating length ($l$).Step 5: RepetitionChange the tension by adding more weights to the hanger (e.g., increase by 50g or 100g).Repeat the process to find the new resonating length for the new tension.Take at least 4-5 sets of readings.CalculationsCalculate the linear mass density ($m$) of the wire by weighing a specific length of the wire coil (Mass / Length).For each set of readings, calculate the frequency using the formula:$$n = \frac{1}{2l} \sqrt{\frac{Mg}{m}}$$Find the mean value of the calculated frequencies to get the result.

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