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

Standing Waves in a String

Section 18.3

PROGRESSIVE WAVES

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.

• Example of transverse waves: vibration of a string, light, water.

ILLUSTRATION

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:

In a longitudinal wave, the particles move back and forth parallel to the wave's direction.

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.

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