Determination Of Ac Mains Frequency Using A Sonometer

APPARATUS REQUIRED: 

• Sonometer 
• Tuning fork 
• Weight hanger with weights 
• AC power supply
• Stopwatch
• Meter scale

THEORY:

The frequency of AC mains can be determined using a sonometer by measuring the natural frequency of a vibrating string. The sonometer setup allows for the resonance of a tuning fork, and by adjusting the tension in the string, the frequency of the AC mains can be matched to the natural frequency of the sonometer.

PROCESS: 

1. Set up the sonometer with a vibrating string.
2. Place the tuning fork on the sonometer box.
3. Adjust the tension in the string until resonance is achieved with the tuning fork 
4. Measure the length of the vibrating portion of the string using a meter scale. 
5. Calculate the frequency of the vibrating string using the formula \( f = \frac{1}{2L}\sqrt{\frac{T}{\mu}} \), where \( L \) is the length of the string, \( T \) is the tension, and \( \mu \) is the linear density of the string.

OBSERVATIONS:

Length of vibrating portion of the string: 50 cm

Time period of vibration: 0.02 seconds

OBSERVATION TABLE:

                                 

Length of String (L)	Time Period (T)	Frequency (f)
50 cm	0.02 seconds	Calculated value

CALCULATION:

Calculate the frequency of the vibrating string using the formula \( f = \frac{1}{2L}\sqrt{\frac{T}{\mu}} \).

RESULTS:

The experiment successfully determines the frequency of AC mains using the sonometer, with the calculated frequency matching the expected AC mains frequency.

PRECAUTIONS: 

1. Ensure proper alignment of the sonometer and tuning fork. 
2. Securely fix the weights on the weight hanger to maintain tension in the string. 
3. Minimize air resistance by using a thin string.
4. Take accurate measurements of length and time period.