Stationary Waves and Progressive Waves
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Transcript of Stationary Waves and Progressive Waves
AMITY UNIVERSITYRAJASTHAN
AMITY SCHOOL OF ENGINEERING AND TECHNOLOGY Presenta
tion onSTATIONARY
&PROGRESSIVE WAVES
Presented by:Ayushmaan Shrivastava Aman Sharma B.Tech(CSE) - I SemBatch 2015-19
Presented to:Dr. Umesh Dwivedi
AMITY UNIVERSITYRAJASTHAN
AMITY SCHOOL OF ENGINEERING AND TECHNOLOGY Presenta
tion on BUILDING POSITIVE ATTITUDE
Presented by:Ayushmaan Shrivastava B.Tech(CSE) - I SemBatch 2015-19
Presented to:Dr. K. C. Barmola
Stationary WavesStationary waves are produced by superposition of two progressive waves of equal amplitude and frequency, travelling with the same speed in opposite directions.
Production of Stationary Waves
A stationary wave would be set up by causing the string to oscillate rapidly at a particular frequency.If the signal frequency is increased further, overtone patterns appear.
Properties of a stationary wave Stationary waves have nodes where there is no displacement at any time.In between the nodes are positions called antinodes, where the displacement has maximum amplitude.
lA vibrating loop
N A N A N
Vibrator
Properties of a stationary wave
The waveform in a stationary wave does not move through medium; energy is not carried away from the source.The amplitude of a stationary wave varies from zero at a node to maximum at an antinode, and depends on position along the wave.
Standing waves in a string fixed at both ends.
Normal modes of a string
... 3, 2, 1,n 2
nL
nl
... 3, 2, 1,n 2
Lvnvf
nn l
Wavelength:
Frequency:
1
... 3, 2, 1,n T2fnfLnf
n
n
Tv :Using
frequency lfundamenta thecalled is T21
1 Lf
Standing waves in a string fixed at both ends.
f1 is called the fundamental frequency
The higher frequencies fn are integer
multiples of the fundamental frequency
These normal modes are called harmonics.
f1 is the first harmonic, f2 is the second
harmonic and so on…
Investigating stationary waves using sound waves and
microwavesMoving the detector along the line between the wave source and the reflector enables alternating points of high and low signal intensity to be found. These are the antinodes and nodes of the stationary waves.The distance between successive nodes or antinodes can be measured, and corresponds to half the wavelength λ.If the frequency f of the source is known, the speed of the two progressive waves which produce the stationary wave can be obtained.
Reflector
DetectorWave source
Factors that determine the fundamental frequency of a
vibrating string
The frequency of vibration depends on the mass per unit length of the string, the tension in the string and, the length of the string.The fundamental frequency is given by
T
Lfo 2
1 where T = tension
= mass per unit length L = length of string
Standing Waves in a String
This is the first normal mode that is consistent with the boundary conditions.
There are nodes at both ends.
There is one antinode in the middle.
This is the longest wavelength mode:
½l1 = L so l1 = 2LThe section of the standing
wave between nodes is called a loop.
In the first normal mode, the string vibrates in one loop.
Section 18.3
Progressive waves are the waves originating from a source and travelling forward in a medium is called a progressive wave.
TRANSVER
SE WAVE
LONGITUDIN
AL WAVES
Two types of progressive waves
TRANSVERSE WAVES:• The waves propagates in the direction
perpendicular to the direction of vibration of particles.
• The waves propagates in the form of crests and troughs.
LONGITUDINAL WAVES:• The waves propagates in the direction parallel to the direction of
vibration of particles.
• The waves propagates as compressions and rarefactions.
• Example of longitudinal waves: sound waves and earthquake waves.
Longitudinal Waves are sometimes called compression waves.
They occur any time a medium is compressed.
As you can see from this diagram :
LONGITUDINAL WAVES:
PROPERTIES OF PROGRESSIVE WAVES
These waves advance in a medium with finite velocity.
All particle of the medium vibrate with same amplitude.
Phase of the vibrations vary continuously from one particle to another.
No particle on the wave is permanently at rest but comes to rest momentarily at its peak or maximum displacement .
Different particles reach the position of maximum displacement at different time.
All particles of the medium pass their mean position in successions but with the same velocity
Pressure variations is same at all points of the medium and travels forward.
These waves transmit energy in medium in direction of propagation.