stationary waves progressive waves dr. anant kumar … · 2020. 9. 15. · investigating stationary...
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STATIONARY WAVES &
PROGRESSIVE WAVES
Dr. ANANT KUMAR SINHAASSOCIATE PROFESSORDEPTT. OF PHYSICSA.M. COLLEGE, GAYA
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Stationary Waves
Stationary waves are produced by superposition of two progressive waves of equal amplitude and frequency, travelling with the same speed in opposite directions.
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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.
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Properties of a stationary wave
A vibrating loop
N A N A N
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.
Vibrator
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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 zeroat a node to maximum at an antinode, and dependson position along the wave.
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Standing waves in a string fixed at both ends.
Normal modes of a string
n 1, 2, 3,...n
n
2L
n 1, 2, 3, ...2L
f v n
v
n
n
Wavelength:
Frequency:
fn
fn n f1
n 1, 2, 3,...n T
2L
TUsing : v
is called thefundamental frequencyT
12L
f 1
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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…
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Investigating stationary waves usingsound waves and microwaves
Moving 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 stationarywave can be obtained.
Reflector
DetectorWave source
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Factors that determine the fundamentalfrequency 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
fo
2L
1 T where T = tension
= mass per unit lengthL = length of string
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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 wavelengthmode:
½= L so = 2L The
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
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Standing Waves in a String
Section 18.3
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Progressive waves are the waves
TRANSVERSE
WAVE
LONGITUDINAL
WAVES
originating from a source and travelling
forward in a medium is called a progressive
wave.
Two types of progressive waves
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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.
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• Example of transverse waves:
vibration of a string, light, water.
ILLUSTRATION
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LONGITUDINAL WAVES:
• The waves propagates in the direction parallel to the directionof
vibration of particles.
• The waves propagates as compressions and rarefactions.
• Example of longitudinal waves: sound waves and earthquake
waves.
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Longitudinal Waves are sometimes called compression waves.
They occur any time a medium is compressed.
As you can see from this diagram :https://drive.google.com/file/d/1nTbCHSSDP6r_gh-ohKlAKuMvqFW80XI6/view?usp=drivesdk
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In a longitudinal wave, the particles move back and forth parallel to the wave's direction.
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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.
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No particle on the wave is permanently at rest but comes to rest momentarily at its peak or maximum displacement .
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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
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Pressure variations is same at all points of the medium and travels forward.
These waves transmit energy in medium in direction of propagation.
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