12. WAVES
Progressive waves
A wave which travels continuously in a
medium in the same direction without a
change in its amplitude is called a travelling
wave or a progressive wave.
14. WAVES
Principle of superposition of waves
When two or more waves cross at a point,
the displacement at that point is equal to
the sum of the displacements of the
individual waves.
The individual wave displacements may be
positive or negative. If the displacements
are vectors, then the sum is calculated by
vector addition.
15. WAVES
Standing Waves
The superposition of two waves travelling in opposite directions ,each having the same amplitude and
frequency is called a standing wave.
16. WAVES
Stationary waves are characterised by nodes and antinodes.
Nodesare the points of the medium which are permanently at rest, i.e. amplitude = 0.
The pressure and density variations at nodes are maximum.
Antinodes are the points of the medium at which amplitude of vibration of particles is maximum.
The pressure and density variations are minimum at antinodes.
17. WAVES
Distance between two consecutive nodes and two consecutive antinodes is λ/2.
Distance between a node and adjoining antinode is λ/4.
18. WAVES
Mode is the name given to any musical sound. The mode of minimum frequency is called
fundamental mode or tone or key mode. The simplest mode of vibration (producing fundamental
note ) is called fundamental mode.
The sounds whose frequencies are greater than the fundamental note are called overtones. When
the frequencies of overtones are integral multiples of the fundamental note ,they are known as the
harmonics.
19. WAVES
Vibrations of stretched strings
Transverse stationary waves are formed on stretched strings. Nodes are formed at the rigid ends ,
where wedges are held under the string.
Antinodes are formed in between, over the stretched string. In any mode of vibration the number
of antinodes is one less than the number of nodes.
The frequency of first overtone or second harmonic is n2 = 2n1
Similarly , the frequency of the second overtone or third harmonic is n3 =3 n1 and so on.
20. WAVES
Organ Pipes
A pipe filled with air having rigid walls and diameter less than its length is called an organ pipe. Such
pipes are used in producing musical sound by pushing air into the pipe. Flute is the best example of an
organ pipe. When the pipe is open at both the ends ,it is called an open organ pipe. When one end of
the pipe is open and the other is closed , it is called a closed organ pipe.
In an open organ pipe , frequency of fundamental note or first harmonic is
21. WAVES
End correction
In organ pipes ,an antinode is not formed exactly at the open end. Rather, the antinode is
formed a little distance (x) away from the open end outside it. This (x) is known as the
end correction. Its value depends upon the internal radius (r )of the pipe. Usually x = 0.6r
Note that in an open organ pipe, end correction is 2x for the two open ends of the pipe.
In a closed organ pipe, end correction is x as there is only for one open end.
22. WAVES
Conclusion
Standing wave or stationary wave is the superposition of two waves travelling in opposite
directions, each having the same amplitude and frequency . The stationary waves are
characterised by nodes (amplitude is 0) and antinodes (amplitude is maximum). Organ pipe is
hollow type pipe in which pipes are used in producing musical sound by pushing air into the pipe.
23. WAVES
The rise and fall in the intensity of sound due to the superposition of two sound waves
of slightly different frequencies traveling in the same direction is known as beats.
Beats
