Determine AC frequency using Melde’s apparatus.

Determine A.C. frequency using Melde’s apparatus and sonometer by studying stationary waves, resonance, and string tension.

Apparatus

An electrically maintained tuning fork, stout cotton thread, light scale pan, weight box, rheostat, step-down transformer, and a frictionless pulley.

Observations

Mass of 1-meter thread (m) = ………… g
Mass of 1 cm thread (m/100) = ………… g
Mass of scale pan (m₁) = ………… g

. Of Obs.	No of loops ‘n’	Distance between extreme nodes ‘d’ cm	Length of scale loop L=d/ncm	Mass of pan and mass added M = m_₁ + m_₂ cm	Tension “T’ T=mgDynes	F4requency of vibration segment f=(1/20) /(T/m)
1 2 3

By arrangement (1) Longitudinal mode

(i) Frequency of A.C. mains =1/2 Frequency of vibrating segment = c /sec .

(ii) Frequency of tuning fork f’1’ =2 x frequency of vibrating = c /sec

(1) Frequency of A.C. mains

(2) Transverse mode

(1) Frequency of A.C. mains =1/2 Frequency of vibrating segment = c /sec .

(i) Frequency of tuning fork =2 x frequency of vibrating = c /sec

Procedure

Begin by connecting the rheostat and switch to the secondary coil of the step-down transformer. Ensure the electromagnet between the tuning fork prongs receives a safe current and the prongs vibrate smoothly. Attach one end of the stout cotton thread to the hook on the fork’s prong, and pass the other end over a frictionless pulley to a light scale pan.

Next, start the tuning fork by connecting the primary coil to the A.C. mains. As the fork vibrates, add small weights to the pan until the thread vibrates in a single loop with maximum amplitude. Gradually change the weights and observe when the thread vibrates in two, three, or more loops.

Measure the distance between extreme nodes to find the total vibrating length. Divide it by the number of loops to calculate the length of one loop. Determine the mass per unit length of the thread (m), and compute the frequency of vibration using the formula:

$\frac{1}{2L} \sqrt{\frac{T}{m’}}$

Arrangements and Modes of Vibration

(1) Longitudinal Mode

Frequency of A.C. mains = ½ × frequency of vibrating segment = …… c/s
Frequency of tuning fork = 2 × frequency of vibrating segment = …… c/s

(2) Transverse Mode

Frequency of A.C. mains = ½ × frequency of vibrating segment = …… c/s
Frequency of tuning fork = 2 × frequency of vibrating segment = …… c/s

In the longitudinal mode, the string completes half a vibration when the fork makes one vibration. In contrast, in the transverse mode, both the tuning fork and the string complete one vibration together, maintaining equal frequencies.

Precautions

Keep the pulley oiled to minimize friction.
Use a uniform, thin thread to ensure equal loop lengths.
Use a lightweight pan and small weights.
Ensure the thread remains horizontal along the fork’s mean position.
Observe that the loops formed are clear and well-defined.

Viva Voce

Q1. What is a Sonometer?
A Sonometer is an instrument with a hollow wooden box over which a wire is stretched to study vibrations.

Q2. Why is it called a Monochord?
It is called a Monochord because it consists of a single vibrating wire.

Q3. What type of waves form along the Sonometer wire?
Transverse stationary waves form along the wire.

Q4. What kind of vibrations occur in the Sonometer wire?
Forced vibrations occur when the wire resonates with the tuning fork.

Q5. Why does a paper rider fly off at resonance?
At resonant length, anti-nodes form where the vibration amplitude is maximum, causing the rider to fly off.

Q6. What is the function of a Monochord?
A Monochord is used to determine the unknown frequency of a tuning fork.