This document describes Melde's experiment to determine the frequency of a tuning fork using standing waves in a stretched string. The experiment investigates both transverse and longitudinal modes of vibration. Results are presented in tables showing the relationship between tension, number of loops, and frequency as tension is varied. Precautions for the experiment are also outlined. Team members contributed by preparing slides on different aspects of the theory, procedure, results and precautions for the experiment.

2. To determine the frequency of electrically maintained tuning fork by
Melde’s experiment
OBJECTIVE OF THE EXPERIMENT

3. Riya Biswas (LEADER)
Aayushi Sinha
Akanksha Kumari Shristi Singh
Mousumi Pradhan
Rohan Sinha
Saprativa Sarkar
Tushar Kumar
Mehul Verma
1.
2.
3.
4.
5.
6.
7.
8.
9.
Team
Members

4.  Standing waves and Normal mode of
Vibration
 Melde’s experiment

5. Standing waves and Normal mode of Vibration
We know 𝜆𝑓 = 𝑣
=>𝑓 =
𝑣
𝜆
𝜆=wave length
𝑓=frequency
𝑣=velocity of wave
Again speed of wave in
stretched string 𝑣 =
𝑇
𝑢
𝑣=velocity of wave
𝑇=tension in string
𝑢=mass per unit length
• The points of the medium which have no displacements
called nodes.
• There are some points which vibrate with maximum amplitude
called antinodes.

6. • The distance between two consecutive nodes is λ/2.
Fundamental Frequency Or First harmonic frequency
We know𝑓 =
𝑣
𝜆
⇒ 𝑓 =
𝑣
2𝑙
and
𝜆
2
= 𝑙 ⇒ 𝜆 = 2𝑙
hence, 𝑓 =
1
2𝑙
𝑇
𝑢

7. Second Harmonic / First Overtone
𝑙 =
2𝜆
2
𝑓 =
2
2𝑙
𝑇
𝑢
Third Harmonic / Second Overtone
𝑙 =
3𝜆
2
𝑓 =
3
2𝑙
𝑇
𝑢
NOTE :
In general (𝑛 − 1)𝑡ℎovertone / 𝑛𝑡ℎharmonic is 𝑓 =
𝑛
2l
𝑇
𝜇

8. 𝑓𝑠= frequence of string
𝑓𝑇= frequency of tuning fork
𝑃 = Number of Loops produced in string
𝑙 = length of thread
T = tension produced in the string
= (Mass of sting + Mass of suspended part)*g
= (M+m)*g
𝑢=mass per unit length
Here we denote -

9. Melde’s Experiment
Used to demonstrate stationary wave in a stretched
string using a large electrically oscillating tuning fork
Two Modes of Vibration
Transverse Mode Longitudinal Mode

10. Transverse Mode
In transverse Mode the string
completes one vibration when
tuning fork completes one
𝑓𝑠 = 𝑓𝑇 =
𝑃
2𝑙
𝑇
𝜇

11. Longitudinal Mode
In Longitudinal Mode the string
completes half of its vibration
when the tuning fork completes
one vibration.
𝑓𝑠 = 𝑓𝑇 =
𝑃
𝑙
𝑇
𝜇

12. NOTE :
• In Transverse mode of vibration, vibration of prongs are in the
direction perpendicular to the length of the string.
• In Longitudinal Mode of vibration, vibration of prongs are in the
direction parallel to the length of the string
• In transverse drive mode the string follows the motion of the tuning
fork, up and down, once up and once down per cycle of tuning fork
vibration. However, one cycle of up and down vibration for
transverse waves on the string is two cycles of string tension
increase and decrease.

13. • The tension is maximum both at the loops’ maximum up position and again at
maximum down position. Therefore, in longitudinal drive mode, since the string
tension increases and decreases once per tuning fork vibration, it takes one
tuning fork vibration to move the string loop to maximum up position and one to
move it to maximum down position. This is two tuning fork vibrations for one up
and down string vibration, so the tuning fork frequency is half the string
frequency.

14. • In both case frequency of Tuning fork is constant
𝑃 𝑇 = Constant
This is called MELDE’S LAW
• In constant frequency if tension increases then number of loops will decrease.
• In constant frequency if tension decreases then number of loops will increase.
• If Melde’s experiment is performed for two different tension in string , say 𝑇1 and
𝑇2 for which stationary waves are obtained with 𝑃1 and 𝑃2 loops in string we can
use
𝑃1 𝑇1 = 𝑃2 𝑇2
𝑃1
𝑃2
=
𝑇2
𝑇1
Hence,

15. 1. Find the mass of the scale pan M' and arrange the
apparatus as shown in figure.
2. Excite the tuning fork by switching on the power
supply (advisable to use voltage more than 6V)
3. Adjust the position of the pulley in line with the
tuning fork.
4. Change the load in the pan attached to the end of
the string.
5. Adjust the applied voltage so that vibrations and
well defined loops are obtained.

16. 6. The tension in the string increases by adding weights in the pan slowly and gradually. For
finer adjustment, add milligram weight so that nodes are reduced to points at the edges.
7. Count the number of loop and the length of each loop. For example, if 4 loops formed in the
middle part of the string If 'L’ is the distance in which 4 loops are formed, then distance between
two consecutive nodes is L/4.
8. Note down the weight placed in the pan and calculate the tension T.
9. Tension, T = (wts on the pan + wt. of pan) g.
10. Repeat the experiment for longitudinal and transverse mode of vibrations.
11. Measure one meter length of the thread and find its mass to find the value of mass produced
per unit length (ms).

17. S.No Weight(Mgm) No. of loops (P)
Length of
thread(cm)
Length of each
loop Tension(M+m)gm Frequency
1 10gm 5 148.5cm 29.7cm 25g 68.8Hz
2 15gm 5 148.5cm 29.7cm 30g 74.8Hz
3 20gm 4 148.5cm 37.1cm 35g 81.4Hz
4 23gm 4 148.5cm 37.1cm 38g 84.2Hz
5 25gm 4 148.5cm 37.1cm 40g 86.4Hz
6 30gm 4 148.5cm 37.1cm 45g 98.4Hz
7 33gm 7 145.8cm 20.8cm 48g 94.0Hz
8 35gm 7 145.8cm 20.8cm 50g 137.9Hz
9 40gm 3 145.8cm 48.6cm 55g 61.9Hz
10 42gm 3 145.8cm 48.6cm 57g 63Hz
11 45gm 3 145.8cm 48.6cm 60g 64.6Hz
Table-1: Frequency of transverse mode arrangement.

19. Graph for Table 1
Mean frequency= 70.04 Hz

20. Table-2: Frequency of longitudinal mode of arrangement
SL
NO.
WEIGHT M
(gm)
NO. OF
LOOPS (P)
LENGTH
OF
THREAD
(cm)
LENGTH OF
EACH LOOP (cm)
TENSION T
(M+m) gm
FREQUENCY(H
z)
1 7 gm 2 8 cm 3.5 cm 10 gm 60 Hz
2 12 gm 2 8 cm 3.5 cm 15 gm 60 Hz
3 15 gm 3 8 cm 3.2 cm 18 gm 60 Hz
4 18 gm 3 8 cm 3.2 cm 21 gm 60 Hz
5 22 gm 3 8 cm 3.2 cm 25 gm 60 Hz
6 24 gm 3 8 cm 3.2 cm 27 gm 60 Hz

21. Voltage= 8v
Mass of pan(m) =3 gm
Mean frequency= 60 Hz

22. A string undergoing transverse vibration illustrates many common to all vibrating
acoustic systems like the vibrations of violin or guitar. The change in frequency
produced when the tension is increased in the string-similar to change in pitch when
a guitar string is tuned-can be measured.
Tuning of instruments like guitar
The vocal organs of human beings form a continuous hallow tube with different
cross sectional areas acting as a filter to regulate the output sound. The interaction
between air flow and the vocal cords periodically opens and closes the glottis,
resulting in a harmonic sound wave, which in fact is the source of the sound.
Human speech analysis
The standing waves formation in strings(Melde’s experiment)can demonstrate that
the formation of waves in air column is the result of reflections of the vibrating air
inside the instrument, and thus sound is produced. These patterns are complex and
usually waves of several frequencies are present.
Standing waves in air column, soprano saxophone, etc.

23. 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.
Precautions :

24. Contribution Of Team Members
Riya Biswas
• Leader of the team
• Application slide-
prepared and
presented
• Editing the ppt.
Aayushi Sinha
• Procedure slide-
prepared and
presented
Shristi Singh
• Precautions slide –
prepared and
presented

25. Contribution Of Team Members
Rohan Sinha
• Transverse wave
Graph slide-
prepared .
• Editing of PPT
Tushar Kumar
• Transverse wave
Graph slide-
prepared and
presented.
• Editing of PPT
Mehul Verma
• Theory slides-
prepared and
presented.

26. Contribution Of Team Members
Saprativa
Sarkar
• Theory slides-
prepared and
presented
Mousumi
Pradhan
• Longitudinal wave
Observation table-
prepared(performed
in virtual lab)
• Longitudinal wave
slides- presented
Akanksha
Kumari
• Longitudinal wave
Graph slide-
prepared

27. THANK YOU