Applied Physics I: Chapter 4: Oscillations and Waves
Frequency of a vibrating string
Let us consider a string of length 'l' fixed between two points AB.
FREQUENCY
OF A VIBRATING STRING
Let
us consider a string of length 'l'
fixed between two points AB as shown in Fig. 4.15.
Let
this string be plucked in the middle at a point 'C' so that it vibrates
transversely only in one segment.
At
the two ends A and B there will be nodes with minimum displacement (or) no
displacement, while in the mid point 'C', there will be an antinode with
maximum displacement.
We
know the velocity of transverse wave is v = √(T/m) …………(1)
If
'n' is the frequency of vibrating string and λ is the wavelength, then, we can
write
Frequency
of the vibrating string n = v/ λ ………..(2)
Substituting
equation (1) in equation (2) we get
n
= 1/ λ . √(T/m)
……………….(3)
When
the string vibrates in one loop as shown in Fig. 4.16, then we can write
AB
= l = λ/2
(or)
λ = 2l ………………..(4)
Substituting
equation (4) in equation (3) we get
n
= 1/2l . √(T/m) ……………….(5)
Equation
(5) is represents the equation for FUNDAMENTAL FREQUENCY.
Laws of transverse vibrations
1) Law of length
The
frequency of transverse vibrations of a stretched string is inversely
proportional to its vibrating length under a constant stretching force.
i.e,
n α 1/l
Where
T & m are constant
2) Law of tension
For
a string of given length and material, the frequency is directly proportional
to the square root of the stretching force (Tension).
i.e.,
n α √T
Where
l, m are constant
3) Law of mass
The
frequency is inversely proportional to the square root of the mass per unit
length, when the tension and the length are kept constant.
i.e.,
n α 1/√m
Where
T, l are constant.
Applied Physics I: Chapter 4: Oscillations and Waves : Tag: Applied Physics : - Frequency of a vibrating string
Applied Physics I: Chapter 4: Oscillations and Waves
Under Subject
Applied Physics I
PH25C01 1st Semester | 2025 Regulation | 1st Semester 2025 Regulation
Related Subjects
English Essentials I
EN25C01 1st Semester | 2025 Regulation | 1st Semester 2025 Regulation
தமிழர் மரபு - Heritage of Tamils
UC25H01 1st Semester | 2025 Regulation | 1st Semester 2025 Regulation
Applied Calculus
MA25C01 Maths 1 M1 - 1st Semester | 2025 Regulation | 1st Semester 2025 Regulation
Applied Physics I
PH25C01 1st Semester | 2025 Regulation | 1st Semester 2025 Regulation
Applied Chemistry I
CY25C01 1st Semester | 2025 Regulation | 1st Semester 2025 Regulation
Makerspace
ME25C04 1st Semester | 2025 Regulation | 1st Semester 2025 Regulation
Computer Programming C
CS25C01 1st Semester | 2025 Regulation | 1st Semester 2025 Regulation
Computer Programming Python
CS25C02 1st Semester | 2025 Regulation | 1st Semester 2025 Regulation
Fundamentals of Electrical and Electronics Engineering
EE25C03 1st Semester | 2025 Regulation | 1st Semester 2025 Regulation
Introduction to Mechanical Engineering
ME25C03 1st Semester | 2025 Regulation | 1st Semester 2025 Regulation
Introduction to Civil Engineering
CE25C01 1st Semester Civil Department | 2025 Regulation | 1st Semester 2025 Regulation
Essentials of Computing
CS25C03 1st Semester - AID CSE IT Department | 2025 Regulation | 1st Semester 2025 Regulation
Applied Physics I Laboratory
PH25C01 1st Semester practical Laboratory Manual | 2025 Regulation | 1st Semester Laboratory 2025 Regulation
Applied Chemistry I Laboratory
CY25C01 1st Semester practical Laboratory Manual | 2025 Regulation | 1st Semester Laboratory 2025 Regulation
Computer Programming C Laboratory
CS25C01 1st Semester practical Laboratory Manual | 2025 Regulation | 1st Semester Laboratory 2025 Regulation
Computer Programming Python Laboratory
CS25C02 1st Semester practical Laboratory Manual | 2025 Regulation | 1st Semester Laboratory 2025 Regulation
Engineering Drawing
ME25C01 EEE Mech Dept | 2025 Regulation | 2nd Semester 2025 Regulation
Basic Electronics and Electrical Engineering
EE25C04 1st Semester ECE Dept | 2025 Regulation | 2nd Semester 2025 Regulation