To Find The Frequency of The AC Mains With a Sonometer

Table of Contents

Aim/Aim of Experiment

To Find the Frequency of the AC Mains with a Sonometer.

Apparatus/Material Required

A Sonometer (with soft iron wire)
A set of eight Tuning Forks
Seven ½ kg slotted weights
A step-down transformer
A Clamp
Rubber pad
Paper rider
A Meter scale.

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.

From the law of length,

V_El₁=V_Tl₂

or V_E=V_T(l₂/l₁)

Hence frequency of alternating current which can be calculated by the given formula,

V=(1/2)V_E=[{(1/2)V_T}l₂/l₁]

The Natural frequency of oscillation for a streched wire of length L mass m and Tension T is given by,

n=1/2L√T/u here u=mass/length = m/L

Diagram

to find frequency of ac mains with
a sonometer — Sonometer in experimental set up to find frequency of AC mains

Procedure

Set up the Sonometer on the table as shown in figure.
Test the pulley and make it frictionless by oiling (if necessary).
Put suitable maximum weights in the hanger.
Move wooden bridges P, P outward to include maximum length of wire (AB) between them.
Decrease the length of the wire by moving both the bridges equally inwardly.
Go on decreasing the length till sonometer wire starts vibrating (a sound is heard).
Switch on the alternating current supply and adjust the length of vibrating portion of AB by sliding the wedge W or W′. Make this adjustment until the amplitude of the vibrating string is maximum.
Measure the length of the wire AB between the edges of the two bridges and record it in ‘length decreasing’ column.
Bring the two bridges closer and then adjust the length for maximum amplitude by increasing it.
Measure the vibrating length and note the tension in the string then record it in length increasing column.
Now take a tuning fork of minimum known frequency and adjust the wire length with the vibrating tuning fork.
Repeat step 11 above with tuning forks of other known frequencies 288-512.
Record the observations.

Observations

The weight suspended to produce on the wire T = ___ kg.
The Length of the Sonometer wire L = ___ m.
Mass of the wire m = ___ kg.
Linear Density u = m/L kg/m.

Observation Table for Frequency and Length:

Frequency of the AC mains with a sonometer observation table

Calculations

Using the formula, v_E = v₂(l₂/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 n=1/2L√T/u for each set of observation and then take the mean, compare it with standard frequency (50Hz).

Result

The frequency of alternating current = ___ Hz.

Percentage Error:

The actual frequency = 50 Hz.
Difference = ___ Hz.
Percentage error = (Difference/Actual Value)×100%

The error is within limits of the experimental error.

Precutions

All the precautions of sonometer experiment should be observed.
Pulley should be as frictionless as possible.
The wire should be of soft iron or of any other magnetic material.
Tip of the electromagnetic pole should be very close to the middle of the sonometer wire.
Length should be noted when the amplitude of vibration is maximum.
After taking each of the observations, circuit should be switched off for a few minutes.

Sources of Error

Friction of the pulley is the main source of error in the experiment, due to this, the value of tension acting on the wire is less than that actually applied, so pulley may not be frictionless.
The wire may not be rigid and of uniform cross-sectional area.
Weights may not be correct.
The knife edges (bridges) may not be sharp.
The AC frequency may not be stable.

Viva Voice Questions with Answers

1. What do you mean by A.C. and D.C.?

Answer: Alternating current (A.C.) is the current whose magnitude changes every instant of time and direction changes periodically. Direct current (D.C.) is the current which has one direction. Steady current is the current whose magnitude and direction does not change with time.

2. How does A.C. differ from D.C.?

Answer: D.C. has same (constant) magnitude and same direction, while A.C. has a changing magnitude and changing direction. D.C. repels but A.C. attract.

3. What is fluctuating current?

Answer: A current having changing magnitude (but not becoming zero) and same direction, is called fluctuating current.

4. What is unidirectional current?

Answer: A current having magnitude changing between maximum and zero and same direction, is called unidirectional current.

5. How is A.C. produced?

Answer: A.C. is produced by dynamo (alternator) in which a coil rotates in a magnetic field.

6. What do you mean by one cycle of A.C.?

Answer: One cycle of A.C. means current from zero becoming maximum positive, then zero, then maximum negative and finally zero again.

7. Why is the instrument called a sonometer?

Answer: Sono means sound. Therefore, a sonometer is an instrument which measures the frequency of sound.

8. What is the unit of frequency of A.C.?

Answer: Unit of frequency of A.C. is hertz (Hz) or per second.

9. What is frequency of alternating current supplied to us in our houses?

Answer: The frequency is 50 hertz (Hz) [hertz means cycles per sec.].

10. What is resonance?

Answer: When the natural frequency of a particle is equal to the frequency of driving force, then resonance takes place. The vibrations are called resonant vibrations.

11. Why does D.C. repel?

Answer: Main line carrying D.C. has same polarity (positive or negative) throughout. On touching it, the body of the person acquires same polarity as that of the main line. The person touching the line is repelled.

12. Why does A.C. attract?

Answer: Main line carrying A.C. as quickly changing polarity. On touching it, the polarity of the body of the person also changes. Due to time lag, the body polarity remains opposite to that of the main line. The person touching the line is attracted.

13. Why A.C. is more dangerous than D.C.?

Answer: It is due to following two reasons: 1. A.C. attracts while D.C. repels 2. A.C. gives a huge and sudden shock which becomes fatal.

14. What is an electromagnet?

Answer: A magnet magnetised by electric current, is called an electromagnet.

15. Which material is used to make sonometer wire and Why?

Answer: Iron. Because it is a ferromagnetic material.

16. What is a timing fork?

Answer: A timing fork is metallic bar bent into U-shape and having a heavy steps attached to the middle of the bent portion.

17. What are stationary waves?

Answer: When two identical waves of same frequency, amplitude travelling in a medium with same speed but in opposite directions superpose, they produce stationary waves.

18. What are nodes and antinodes?

Answer: Nodes are the points of zero amplitude and antinodes are points of maximum amplitude.

19. Define wavelength for a stationary wave.

Answer: The distance between the centres of two successive crests or troughs is called the wavelength of a stationary wave.

20. Why does the string of the sonometer vibrate?

Answer: When the vibrating tuning fork is kept on the board of the sonometer, the forced vibrations of the board communicate energy to the string which in turn is set into forced vibrations.

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