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AimTo determine the frequency of AC mains using a sonometer.
Apparatus requiredA 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
TheoryConsider the frequency of the alternating current to be v, so that the frequency of magnetisation of the electromagnet VE becomes 2v. Let a loaded stretched soft iron wire have a resonant length l1 with the electromagnet. Let a tuning fork of frequency VT have resonant length l2. According to the law of length,
l1/l2 = √(density of wire/density of steel) x √(tension in wire/tension in steel)
Hence, the frequency of the alternating current is calculated using the formula
v = VT x √(density of wire/density of steel) x √(tension in wire/tension in steel) x (l2/l1)²/2
The natural frequency of oscillation for a stretched wire of length L, mass M and tension T is given by
VT = 1/(2L) x √(T/M)
ProcedureConnect the sonometer wire to one of the bridges of the sonometer box.
Connect the electromagnet or tuning fork to the other bridge of the sonometer box.
Connect the frequency meter or oscilloscope to the output of the sonometer box.
Adjust the sonometer wire to a length equal to half of the wavelength of the sound produced by the electromagnet or tuning fork.
Connect the sonometer wire to the AC mains using connecting wires.
Turn on the AC mains.
Adjust the frequency meter or oscilloscope to measure the frequency of the sound produced by the electromagnet or tuning fork.
Note down the frequency displayed on the frequency meter or oscilloscope.
Repeat the above steps with different lengths of the sonometer wire.
Observation and ResultCalculation: The frequency of the AC mains can be calculated by using the formula:
f = (n/2L) * v
Where, f = frequency of the AC mains n = number of loops in the sonometer wire L = length of the sonometer wire v = speed of sound in air (taken as 340 m/s)
Result: The frequency of the AC mains can be determined accurately by this method.