Sonometer: Laws of Transverse Vibrations

Understanding resonance in stretched strings and AC frequency.

Principle of Sonometer

A Sonometer works on the principle of Resonance. When a stretched string vibrates, it produces transverse waves. If the natural frequency of the string matches the frequency of the external driving force (electromagnet), the amplitude of vibration becomes maximum.

Condition for Resonance: Natural Frequency of String = Frequency of AC Mains.

The Mathematical Formula

$$ n = \frac{1}{2l}\sqrt{\frac{T}{m}} $$

n: Frequency of AC Mains (Hz)
l: Resonant Length (m)
T: Tension = Mass × Gravity (N)
m: Linear Mass Density (kg/m)

Viva Voce & Practical Concepts

Q: Why does the paper rider fall off?

A: At resonance, the amplitude of vibration is maximum at the antinodes (center of the wire). The violent vibration throws the light paper rider off.

Q: Why use an Electromagnet?

A: The electromagnet provides a periodic driving force with the same frequency as the AC mains (50Hz), causing the magnetic wire to vibrate.

Q: What are the laws of transverse vibrations?

1. Law of Length ($ n \propto 1/l $)
2. Law of Tension ($ n \propto \sqrt{T} $)
3. Law of Mass ($ n \propto 1/\sqrt{m} $)

Observations

Mass (g)	Tension (N)	Length (cm)	l²
No readings recorded yet.

Graph: Length² vs Tension

Slope Calculation Active

Calculated Frequency: -- Hz