The document describes an experiment to measure the Young's modulus of a brass bar using flexural vibrations. A brass bar clamped at one end is connected to a signal generator and power amplifier. The frequency is varied from 10-100Hz while monitoring the amplitude to determine the fundamental frequency of vibration. The reciprocal of the fundamental frequency is plotted against the square of the length of the bar to determine the slope and calculate Young's modulus. The experiment is also used to measure the rigidity modulus of a brass wire.

1. YOUNG’S MODULUS OF BRASS BY
FLEXURAL VIBRATIONS OF BAR

2. MODULUS AND ITS TYPES
• It is ratio of stress to the corresponding
strain within the elastic limit.
• Its types are-
• Young’s modulus
• Rigidity modulus
• Bulk modulus

3. YOUNG’S MODULUS
• Within the elastic limit , the ratio of
longitudinal stress to the longitudinal strain is
called the young’s modulus.
• 4π2

4. AIM: To verify that the fundamental
frequency of vibration of a steel bar clamped at
one end is inversely proportional to the square
of its and to measure the Young’s modulus of
the bar.
APPARATUS REQUIRED
• Signal generator, power amplifier , Young’s
modulus setup, multimeter

5. PROCEDURE
• The bar is clamped so that the length of the
bar from free end is 20cm.
• The signal generator is put in the frequency
range 10-100Hz.
• The amplitude knob is turned towards right
and the max value is noted on the multimeter.
• Then turn the frequency knob to a frequency
nearly six times the fundamental frequency.

6. • Plot a graph of 1/f1 against l2. Measure the
slope α calculate young’s modulus.
• Next calculate f2/f1 and find average.

7. RIGIDITY MODULUS
• It is defined as the ratio of tangential stress to
the shear strain within the elastic limit.
• When a material is elongated along the X-axis
it suffers a contraction in the perpendicular
direction . This is called poisson’s ratio(σ).
• σ =(∆y/y)/(∆x/x)

8. PROCEDURE
• Fix the movable clamps on either side of the
center of the wire so that they are at a distance
of 20 cm from the center of the brass wire.
• Connect the signal generator to the power
amplifier.
• The output of the power amplifier is connected
to the wires from the coils on the experimental
set up.
• Note the frequency at which amplitude is
maximum.The length is changed from 20 to 8cm.