To Find The Frequency Of AC Mains With A Sonometer

Aim

To determine the frequency of AC mains using a sonometer.

Apparatus

• A sonometer with soft wires
• A set of eight tuning forks
• Seven ½ kg slotted weights
• A set of eight tuning forks
• Clamp
• Rubber Pad
• Paper rider
• Metre Scale

Diagram

Theory

Let us consider the alternating current to have a frequency v so that the frequency of magnetisation of the electromagnet V_E becomes 2v.

Let a loaded stretched soft iron wire have a resonant length l₁ with the electromagnet. Let a tuning fork of frequency V_T have resonant length l₂.

According to the law of length,

Hence, the frequency of the alternating current is calculated using the formula

The natural frequency of oscillation for a stretched wire of length L, mass M and tension T is given by

Procedure

1. Place the sonometer on the table as shown in the figure.
2. Test the pulley and make it frictionless by oiling.
3. Put suitable weights in the hanger.
4. Move the wooden bridge P outward to include the maximum length of wire AB.
5. Decrease the length of the wire by moving the wooden bridges equally inwardly.
6. Go on decreasing the length till the sonometer wire starts vibrating.
7. The length of the wire can be adjusted for the maximum amplitude of vibration.
8. Measure the length of the wire AB between the edges of the two bridges and record it in length decreasing columns.
9. Bring the bridges closer and adjust the length for the maximum amplitude by increasing it.
10. Measure the length and record it in length increasing column.
11. Now take a tuning fork of minimum known frequency and adjust the wire length with the vibrating tuning fork.
12. Repeat step 11 above with tuning forks of other known frequencies.
13. Record your observations.

Observation

The weight suspended on the wire, T = _____ kg.

The length of the sonometer wire, L = _____ m.

Mass of wire, m = _____ kg.

Linear density,

Table for frequency and length

Calculations

Using the formula, v_E = v₂l₂/l₁, calculate v_E with observations 2 to 7.

Record these values in column 4 of the table.

Find the mean of the above six values of v_E.

Then the frequency of the alternating current can be determined by the formula,

v = v_E/2

Use

Result

The frequency of the alternating current is _____ Hz.

Percentage Error

The actual frequency = 50 Hz

Difference = _____ Hz

The error is within limits of experimental limits.

Precaution

1. The wire should be soft iron or any other magnetic material.
2. Length should be noted when the amplitude of vibration is maximum.
3. Tip of the electromagnet should be very close to the wire in its middle

Viva Voce

1. How does AC differ from DC?

Ans: DC has the same magnitude and direction throughout, while AC has to change magnitude and direction.

2. What is resonance?

Ans: When the natural frequency is equal to the frequency of the driving force, then resonance takes place. These vibrations are known as resonant vibrations.

3. Why is AC more dangerous than DC?

Ans: It is dangerous due to the following reasons:

1. AC attracts while DC repels

2. AC gives a huge and sudden shock that can be fatal.

4. What is the skin effect?

Ans: In an alternating current, the moving electrons tend to drift towards the conductor’s surface while moving along its axis. This tendency increases with the frequency of A.C in very high-frequency A.C. Electrons flow only on the conductor’s surface. This phenomenon is known as the skin effect.

5. When will the wire resonate?

Ans: When the frequency of A.C mains is equal to the natural frequency of the vibration of the wire.

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