STATIONARY WAVES &

PROGRESSIVE WAVES

Dr. ANANT KUMAR SINHAASSOCIATE PROFESSORDEPTT. OF PHYSICSA.M. COLLEGE, GAYA

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.

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

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

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.

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

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 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

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

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

Standing Waves in a String

Section 18.3

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

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 directionof

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 :https://drive.google.com/file/d/1nTbCHSSDP6r_gh-ohKlAKuMvqFW80XI6/view?usp=drivesdk

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

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.