To determine the frequency of an electrically driven tuning fork.

Aim

To determine the frequency of an electrically driven tuning fork.

Apparatus Required:

An electrically maintained tuning fork ,a light smooth pulley fixed to a stand, a light scale pan, thread, a storage cell, rheostat, plug key and connecting wires.

Description::

A fork can be maintained in the state of continuous vibration electrically. One terminal of the coil of an electromagnet is connected to the make and break arrangement and the other end of the coil to the cell, rheostat and plug key connected in series. In the normal position when the circuit is closed, the electromagnet attracts the prong of the fork towards it. This breaks electrical circuit and the prong moves back closing the circuit. The electromagnet again attracts the prong towards it. This is repeated again and again and the fork is maintained in a state of continuous vibration. One end of the thread of length about 3 meters is joined to a screw attached to one prong of the fork and the other end is passed over a small pulley and a light pan is fixed at the other end of the thread. When the fork is vibrated electrically, stationary waves of well-defined loops are formed. Melde's apparatus can be arranged in two modes of vibration,

Transverse Mode

When the direction of motion of the prong is at right angles to the length of the string, the vibrations of the thread represent the transverse mode of vibration.

Procedure:

1. The apparatus is arranged in transverse mode of vibration of the thread as shown above. A suitable load is placed in the scale pan. The tuning fork is excited electrically. The length of the thread is adjusted by moving the pulley until well defined loops are formed in it. The distance between a definite numbers of well-defined loops is measured with a meter scale from which the average length l of a single loop is determined.
2. The total load attached to the thread inclusive of the mass of the pan is noted. If it is Mgm, the tension applied on the string is T= Mg = (M’+M”) g. Where g is acceleration due to gravity. M’ is the mass added in the pan and M” is the mass of pan.
3. The mass of the thread (about 5 mts in length) is determined correct to a milligram. The mass per unit length of the string (m) is then determined. The frequency of the tuning fork is found by the relation


N = 1/2ι√T/m = 1/2√m √T/ι

4. The experiment is repeated for various tensions and the observations are tabulated in table (i) and N is calculated

Observations:

M' = mass kept in the pan in grams

M” = mass of the pan

m = linear density

Formula for calculation N = 1/2√m (Average √T/ι)

Longitudinal Mode

When the direction of motion of the prong is along the length of the thread, the vibrations of the thread represent longitudinal mode of vibration.

Procedure: -

1. The apparatus is arranged in longitudinal mode of vibration of the thread. The experiment is done in similar manner as in 1. The average ι of the loop, the tension T applied to the thread and the mass per unit length of the thread (m) are found. The frequency of the tuning fork is found by the relation

N = 1/ι√T/m = 1/√m √T/ι

The experiment is repeated with different tension and the observations are tabulated in table (ii) and are calculated.

Observations:

Average √T/ι = -------------

Mass per unit length of the thread (m) =---------------gms.

M' = mass kept in the pan in grams

M” = mass of the pan

m = linear density

Formula for calculation N = 1/√m (Average √T/ι)

Precautions:

1. A thin long and inelastic thread should be used.
2. The loops should be well defined and confined to a single plane.

Result:

The frequency of the tuning fork in transverse mode = Hz

The frequency of the tuning fork in longitudinal mode = Hz

The mean of the two average frequencies in the transverse and longitudinal modes gives the correct frequency of the tuning fork.