This document presents the results of an experiment to verify the laws of transverse string vibration and determine the frequency of a tuning fork using Melde's experiment. The experiment involved stretching a string between fixed points and vibrating it with a tuning fork to create standing waves. Measurements were taken of the string tension, length, and number of loops at different tensions. The data was analyzed and found that the frequency of the tuning fork was 53.456 vibrations/second, verifying the laws of transverse string vibration. In conclusion, the experiment was a success in measuring the tuning fork frequency through creating and analyzing standing waves on a vibrating string.

1. WELCOME TO
PHYSICS 2 LAB
PRESENTATION
Verifying the Laws of Transverse
Vibration of Strings and to Determine
the Frequency of a Tuning Fork by
Melde’s Experiment
Course Instructor: DR. SHOVAN KUMAR
KUNDU
Presented By Group-08
OBYEDUL HAQUE EFTY (22-47242-1)
MD. TASNIM AHMED (22-47187-1)
ARUP SAHA (22-47121-1)

2. TABLE OF
CONTENTS
1 THEORY
2 APPARATUS
3 PROCEDURE
4 DATA TABLE
5 ANALYSIS OF DATA & CALCULATION
6 DISCUSSION
7 REFERENCES

3. OBJECTIVES
The main objective of this lab was to
Verifying the Laws of Transverse
Vibration of Strings and to Determine the
Frequency of a Tuning Fork by Melde’s
Experiment.

4. V
ܶ
Natural frequency is the frequency at which a system tends to oscillate in the
absence of any driving or damping force.
Resonance occurs when the frequency of the applied periodic system is equal to
one of the natural frequencies of the oscillating system.
The oscillation of a device at its normal or unforced frequency is the resonant
frequency.
For this experiment the string will be set into vibration by setting the tuning
fork into vibration.
As a result, waves will proceed along the string.
The superposition of the direct and reflected waves will form stationary waves,
in which extreme fixed ends of the string will always be nodes and in between
them there may be one or more antinodes depending on the tension to which the
string is subjected or the length of the string.
When resonance occurs between the fork and the string by adjusting the forks
frequency equal of the fundamental or any one of the higher tones.
Theory

5. V
ܶ
 We see standing wave is formed and loops are clearly specified.
For fundamental frequency, wavelength(λ)=2l, where l is the length of
the string.
 The frequency of the fork will be given by the relation,
f =
1
λ
√(
τ
µ
)
where µ is the mass per unit length of the vibrating string and τ is the
tension applied to the string.(transverse mode)
 In transverse mode, string has the same frequency of the tuning fork .
This happens due to how tension is applied to the string from the
vibration of fork in different position.
Transverse case,
f =
1
2l
√(
τ
µ
) and,
τ
l2 = 4µf2 = constant
By changing the tension and length of the string, the frequency of the
tuning fork can be determined.
Theory

6. APPARATUS
Melde’s apparatus
Weight box
Meter scale
String, etc.

7. PROCEDURE
 Weighted the scale pan and clamped the tuning fork at the edge of the table.
 Weighted the string and measured the length of determine the mass per unit length.
 Fixed a pulley over a clamp, screwed at other edge of the table.
 Fasten a thread to the tip of the prong and passed the other end over the pulley.
 Hanged the scale pan to this end with some weights so that the string is lightly stretched.
 Rotated the screw of an electrically maintained tuning fork to generate vibration.
 Increased the weights until loops are maximum, the nodal points are fixed in position and the loops are equal length,
also loops can be controlled by adjusting the length of the string.
 To get the length of two successive nodes, we divide the length of the string by the number of loops.
 Increased the weight in the scale pan by 20gm and then 50 gm to change the number of loops.
 Calculated the frequency of the tuning fork in transverse position using the equation, f =
1
2l
√(
τ
µ) .

8. No. of
observations
Total no of
loops
between
the fixed
ends(N)
Load on
the scale
pan,
Wt(gm)
Tension,
τ=(W+Wt)
g
(dynes)
Distance
between the
fork and the
pulley(S)
(cm)
Length of
a segment,
l=G/N
(cm)
Frequency of
the fork,
f’=
1
2l
√(
τ
µ
)
(vibrations/
second)
Mean
frequency, f
(vibrations/
Second)
τ
l2 =
constant
1 2 0 23324 49 24.6 53.608
53.456
38.51
38.25
2 2 20 42924 67 33.5 53.426
3 2 40 62524 81 40.5 53.335 38.12
DATA TABLE, ANALYSIS OF DATA & CALCULATION
(A)Mass of the scale pan, w = 23.8 gm
(B) Length of the string, L = 149 cm
Mass of the string, M = 0.5 gm
So, the mass per unit length of the thread, µ =
M
L
= 3.3557×10−3 gm/cm
∴ µ = 3.3557×10−3 gm/cm

9. RESULT
The law of transverse vibration of string is verified by showing
τ
l2 = constant and the frequency
of the tuning fork is 53.456 Vibration/sec.
Frequency of the fork,
𝑓 = 53.456 𝑣𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛/𝑠𝑒𝑐

10. DISCUSSION
1
2
3
4
5
We found out that, the frequency of the tuning fork is 53.456 vibrations/second. It signifies that, the
tuning fork completes 53.456 full cycles in a single second.
There is some error due to mechanical friction and measuring errors.
It was a very informative lab experiment because we have got the proper understanding of wave
reflection, super position of waves and construction of standing waves.
We also find out that the ratio of tension and square of the length of a loop is nearly constant in all the
observations.
So indeed the laws of transverse vibration of string is verified. The experiment accomplished and it was a
great learning lesson for us.

11. REFERENCE
S
Fundamentals of Physics: Transverse and Longitudinal waves (Chapter:16, Page:445), Waves
on a stretched string (Chapter:16, Page:452), Standing wave and resonance (Chapter:16,
Page:465).
Video Link:
Transverse and Longitudinal modes of vibration:
https://www.youtube.com/watch?v=0Anh9HthWgQ
Melde’s Experiment:
https://www.youtube.com/watch?v=hwWPDqHFxOg

12. THANK
YOU
Any Question..?
Presented by Group-08