PHY119: Engineering Physics Laboratory
Melde’s experiment
Deepak Kaushik
Department of Physics
School of Chemical Engineering & Physical Sciences
Lovely Professional University, Punjab.
deepak.23309@lpu.co.in
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AIM: To find the frequency of ac mains using electric vibrator.
Learning Objectives
1. Learn about formation of standing waves and their dependence on various
parameters.
2. Understand the concept of magnetic field produced by solenoid in response to
alternating current.
3. Visualize the nodes and antinodes.
April 22, 2021 PHY119 (ENGINEERING PHYSICS LAB)
Basic Understanding
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Melde’s Experiment
It is a scientific experiment carried out in 1859 on
the standing waves produced in a tense cable
originally set oscillating by a tuning fork, later
improved with connection to an electric vibrator.
Franz Melde
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Melde’s Experiment
• Aim: To demonstrate the interference of
mechanical waves
• Mechanical waves moving in opposite direction
between fixed points form standing waves
• Standing waves were first discovered by Franz
Melde, who coined the term "standing wave" Franz Melde
around 1860
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Standing waves
A standing wave or a stationary wave,
is a wave which oscillates in time
but
whose peak amplitude profile does not move
in space
These waves are produced by waves moving in
opposite directions
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Anti-node:
Region of maximum
amplitude in a standing wave
𝝀 Node:
𝟐 Region of minimum
amplitude in a standing wave
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Standing waves and resonance
• At ordinary frequencies, waves travel
backwards and forwards along the string or
any media/vacuum
• However, at certain special frequencies, the
interference produces strong standing wave
patterns.
• Such a standing wave is said to be produced
at resonance.
• This phenomenon is called RESONANCE.
• These certain frequencies are called
resonant frequencies.
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Experimental Setup
Apparatus: Electric vibrator, pulley, string, pan, weights, scale
𝑀𝑔 = 𝑇
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Influence of various parameters on standing wave characteristics
𝑇 𝑀𝑔 𝑀𝑔𝐿
Speed of wave in stretched string is 𝑣= = =
𝜇 𝜇 𝑚
Here,
T – Tension in the string = Mg
μ - (M/L) Linear density or mass per unit length of the string.
L – Length of the string
M - Mass suspended
g - Acceleration due to gravity 𝜆
For standing waves, 𝒍 = ⇒ 𝜆 = 2𝑙
2
𝑣
frequency 𝑓=
𝜆
1 𝑀𝑔𝐿
𝑓=
2𝑙 𝑚
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Significance:
1. Tuning of musical instruments like guitar, violin.
2.Frequency of tuning forks
3. Standing waves in air column, soprano saxophone etc.
4. Human speech analysis.
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Direct vs alternating current
f = 0 Hz
f = 50 Hz
We have verify this using Melde’s experiment
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Activity
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Step by Step guide to perform the experiment on
Virtual platform
(1) Link: https://ophysics.com/w8.html
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Home page to start experiment
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Step 1
Fix vibration frequency to 50 Hz
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Step 2
Set linear density of string here 17
Step 3
Change the tension so that loops are formed and their amplitude is maximum
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Green area shows limits within which the loops are to be counted
Red areas show limits where loops are NOT to be counted
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Q. How many loops are there in this picture??
2 4 6
1 3 5 7
Answer 7
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How many loops are there in this picture??
1 2 3 4 5 6 7
7 21
Alternate way to count loops
1. Count number of peaks 2. Count number of valleys 3. Add these two numbers
3 4 3+4 = 7
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Sample calculation
Length of String, L = 4 m
No. of loops, n = 7
1 𝑇 1 10.41 57.03
𝐿 4 𝑓= = = = 50.03 𝐻𝑧
Length of each loop, 𝑙 = = = 0.57 𝑚 2𝑙 𝜇 1.14 3.2 × 10−3 1.14
𝑛 7
Wavelength, 𝜆 = 2𝑙 = 2 × 0.57 = 1.14 𝑚
𝜇 = 3.2 × 10−3 𝑘𝑔/𝑚
Tension, T = 10.41 N 23
Name: Registration No. Date of performance:
Section: Group:
Observations:
Total length of the string = ____m
Linear mass density of the string, 𝝁 = ______ kg/m
Set value of frequency = ____ Hz
• Aim
Frequency,𝑓 = • Learning objectives
Length of loop,
1 𝑇 • Apparatus
S. No. Tension, T (N) No. of Loops, n 𝑙 = 𝐿/𝑛
2𝑙 𝜇 • Theory
(m)
(𝑯𝒛) • Diagram
1. • Formula
• Observations
2. • Calculations
3. • Results
• Error analysis
4.
• Learning outcomes
5. • References
𝑓1+𝑓2+ ....... ... ... .𝑓𝑛
𝐀𝐯𝐞𝐫𝐚𝐠𝐞 𝐯𝐚𝐥𝐮𝐞 𝐨𝐟 𝐟𝐫𝐞𝐪𝐮𝐞𝐧𝐜𝐲 =
𝑛
= _____ Hz
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Additional links
https://www.youtube.com/watch?v=hwWPDqHFxOg
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