Melde's Experiment investigates the frequency of an electrically maintained tuning fork through longitudinal and transverse modes of vibration. Conducted with a tuning fork, weights, and thread, this experiment provides insights into the principles of sound and vibration. It is designed for physics students exploring wave mechanics and resonance. The procedure includes measuring loop lengths and calculating frequencies based on applied tension and mass. This hands-on approach enhances understanding of vibrational modes and their applications in acoustics.

Key Points

  • Explores the frequency of tuning forks in longitudinal and transverse vibrations.
  • Includes detailed procedures for measuring loop lengths and calculating frequencies.
  • Utilizes an electrically maintained tuning fork and various weights for experimentation.
  • Designed for physics students studying wave mechanics and resonance.
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Melde’s Experiment
Object: To determine the frequency of electrically maintained tuning fork by means of Melde’s apparatus in
longitudinal and transverse mode of vibration.
Apparatus used: electrically maintained tuning fork, hanger/pan and weights (5, 10, 20 gm) and thread.
Formula Used:
A. Longitudinal mode of vibration: The
frequency of electrically maintained tuning fork in
longitudinal mode of vibration is determined by
following formula.
m
T
l
p
n =
(1)
B. Transverse mode of vibration: The frequency
of electrically maintained tuning fork in transverse
mode of vibration is determined by following
formula.
m
Mg
l
p
n
2
=
(2)
Where l = loop length of the thread
T = tension applied to the wire=Mg,
M= total mass loaded on thread
m = mass per unit length of the thread,
Fig.1: Electrically maintained tuning fork
Figure and Circuit:
Fig.2: Arrangement for transverse mode of vibration
D.K.Pandey
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Fig.3: Arrangement for longitudinal mode of vibration
Procedure:
1. Connect the primary of the step down transformer to A.C mains, while the secondary to the given point of
electrically maintained tuning fork.
2. Tight the one end of thread to the prong of tuning fork and other end to a scale pan. Hang the scale pan with
pulley that is fixed at end of table.
3. Arrange the electrically maintained tuning fork in transverse situation (Fig.2) (i.e. arrange in such a way that
length of string is parallel to the prong of tuning fork) and load a mass of 5gm on its pan. Now rotate the
screw S (i.e. excite the tuning fork), so that vibration in tuning fork gets started.
4. Move the tuning fork toward or away from pulley to adjust the length of thread, so that loops could be
formed. Now measure the length thread for one and two loop when stable loops are formed in horizontal
plane. This will give the value l for one and two loops.
5. Now increase the mass on scale pan (m=10, 20 gm) and repeat the step 4.
6. After it arrange the electrically maintained tuning fork in longitudinal situation (Fig.3) (i.e. arrange in such a
way that length of string is perpendicular to the prong of tuning fork) and load a mass of 5gm on its pan.
Excite the tuning fork, so that vibrations get started in tuning fork.
7. Move the tuning fork toward or away from pulley to adjust the length of thread, so that loops could be
formed. Now measure the length thread for one and two loop when stable loops are formed in transverse
plane. This will give the value l for one and two loops. The observed length should come double length of
transverse case.
8. Now increase the mass on scale pan (m=10, 20 gm) and repeat the step 7 for this arrangement.
9. Find out length of thread per loop (l/p) for each case of load.
10. Measure the mass (m
T
) of 10m length of thread and mass of scale pan (m
P
). Value of m
T
/10 gives mass per
unit length of thread.
11. Calculate frequency of tuning fork for transverse and longitudinal case using M, m and l/p,
D.K.Pandey
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Observation:
1. Table for transverse mode of vibration
Sr.
No.
Mass loaded
on pan, m
(gm)
Mass
of pan, m
P
(gm)
Total mass
M=m+m
P
(gm)
No. of
Loops
(p)
Loop
Length, l
(cm)
l/p
Mean
l/p
1
1 5
2
1
2 10
2
1
5 20
2
2. Table for longitudinal mode of vibration
Sr.
No.
Mass loaded
on pan, m
(gm)
Mass
of pan, m
P
(gm)
Total mass
M=m+m
P
(gm)
No. of
Loops
(p)
Loop
Length, l
(cm)
l/p
Mean
l/p
1
1 5
2
1
2 10
2
1
5 20
2
3. Mass per unit length of thread (m)=……gm/cm
Calculation: Calculate the frequency for each mass and mode of vibration using expressions (1) and (2).
Take mean of frequencies of both longitudinal and transverse case.
Result: The frequency of electrically maintained tuning fork in transverse arrangement = ………..Hz
The frequency of electrically maintained tuning fork in longitudinal arrangement= ………..Hz
Mean frequency of electrically maintained tuning fork= ………..Hz
Precautions:
1. The thread should be uniform and inextensible.
2. Friction in pulley should be small. Otherwise it causes the tension to be less than the actual applied
tension.
3. The loops in central part of thread should be counted for measurement. The nodes at pulley and tip of
prong should be neglected as they have some motion.
4. The longitudinal and transverse arrangements should be correct otherwise the length measured will be
wrong.
D.K.Pandey
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FAQs

What is the purpose of Melde's Experiment?
Melde's Experiment aims to determine the frequency of an electrically maintained tuning fork by examining its behavior in both longitudinal and transverse modes of vibration. By using a tuning fork, weights, and thread, students can observe how different masses affect the frequency of the vibrations. This experiment illustrates fundamental concepts in wave mechanics and resonance, making it a valuable educational tool for physics students.
What apparatus is used in Melde's Experiment?
The apparatus for Melde's Experiment includes an electrically maintained tuning fork, a hanger or pan for weights, and a thread. The tuning fork is excited to produce vibrations, while the weights are used to apply tension to the thread. This setup allows for the observation of loop formations in the thread, which are crucial for measuring the frequency of the tuning fork in both longitudinal and transverse modes.
How is frequency calculated in Melde's Experiment?
Frequency in Melde's Experiment is calculated using specific formulas derived from the tension applied to the thread and the mass loaded on the pan. For the transverse mode, the formula involves the loop length and the mass per unit length of the thread. In the longitudinal mode, a similar approach is taken, with adjustments made for the orientation of the tuning fork. These calculations help students understand the relationship between mass, tension, and frequency.
What are the key observations in Melde's Experiment?
Key observations in Melde's Experiment include measuring the loop lengths formed in the thread when the tuning fork vibrates. Students observe how the number of loops changes with varying weights and how this affects the frequency of the tuning fork. The experiment also highlights the differences between longitudinal and transverse vibrations, providing a comprehensive understanding of wave behavior.
What precautions should be taken during Melde's Experiment?
Precautions during Melde's Experiment include ensuring that the thread used is uniform and inextensible to obtain accurate measurements. Additionally, minimizing friction in the pulley is crucial, as excessive friction can lead to incorrect tension readings. Students should also focus on counting the loops in the central part of the thread, avoiding nodes at the pulley and prong tips, which may not exhibit stable motion.

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