aim, theory, procedure and analysis

1. MELDe’S
EXPERIMENT
By --
GAGANA G S

2. HERE IN THIS EXPERIMENT WE ARE GOING TO DETERMINE THE
FREQUENCY OF AN ELECTRICALLY MAINTAINED TUNING FORK BY
1) TRANSVERSE MODE OF VIBRATION
2) LONGITUDINAL MODE OF VIBRATION

3. THEORY:
1) SPEED OF WAVES IN STRETCHED STRING
2) VIBRATIONS OF THE STRETCHED STRING
3) TRANSVERSE DRIVE MODE
4) LONGITUDINAL DRIVE MODE

4.  SPEED OF A WAVE IN STRETCHED TRING
A string mean a wire or fiber which has a uniform diameter
and which is perfectly flexible. The speed of a wave in a
flexible stretched string depends upon the TENSION in the
string and MASS PER UNIT LENGTH (DENSITY) of the string,
v = ( T / M )^1/2
where, T => tension in the string = mg
m = total mass suspended
g = acceleration due to gravity.
M => linear density = m’ / L
m’ = mass of the string
L = total length of the string.

5.  VIBRATIONS OF STRETCHED STRING:
When the string is clamped to a rigid support, transverse
propagative waves travel towards each end of the wire. By the
superimposition of the incident and reflected waves, transverse
stationary waves are set up in the wire. Since the ends of the
wire are clamped, there is node at each end and antinode in the
middle as in fig.
The distance b/w two consecutive nodes is
l = /| / 2
frequency of the vibration of the string is
f = v / /| = v / 2l
=> f = 1 / 2l * ( T / M )^1/2 Hz.

6.  TRANSVERSE MODE OF VIBRATION;
In this mode the vibrations of the prongs are in the direction
perpendicular to the length of the string. The time during which the
tuning fork completes one vibration, the string completes its one
motion, i.e. the frequency of the string is equal to the frequency of the
tuning fork.
=> f = 1 / 2l * ( T / M )^1/2 Hz.

7. LONGITUDINAL MODE OF VIBRATION :
In this arrangement the tuning fork is set in such a way that the
vibrations of the prongs are parallel to the length of the string. The
time during which the tuning fork completes half of its vibration. In this
mode frequency of the tuning fork is twice the frequency of the string.
Hence the equation for the frequency is
f = 1 / l (T / M ) Hz.

8. EXPERIMENTAL SET UP

10. 1) Select the mode of vibration.
2) The transformer voltage is adjusted to 8v.
3) Mass is suspended in the scale pan.
4) Power on and form the loops.
5) Length will be measured by using the scale.
6) Using the equations for respective modes of
vibration calculate the frequency of a tuning fork
7) Repeat the experiment by changing the
parameter.

11. OBSERVATIONS AND CALCULATION:
SI. NUMBER. TOTAL MASS
M
(in kg)
TENSION T
(in kg ms^2 )
LENGTH l
B/W NODES
(in cm)
MEAN
LENGTH l
(in cm)
l^2
(in cm^2)
FREQUENCY
(in Hz)
1 0 0.1274 58 58 3364 50.24
2 100 0.1284 58.1 58.1 3375.61 50.357
3 200 0.1294 58.2 58.2 3387.24 50.46
4 300 0.1303 58.3 58.3 3398.89 50.55

12.  MODEL GRAPHS:
TRANSVERSE MODE LONGITUDINAL MODE

13. 1) FOR TRANSVERSE MODE:
f^2 = 1/4µ * 1/ slope.
2) FOR LONGITUDINAL MODE:
f^2 = 1/µ * 1/slope.

14. RESULT:
FREQUENCY OF THE ELECTRICALLY
MAINTAINED TUNING FORK IS FOUND TO BE
50 Hz.