Interference;(i)As a result of superposition of two waves of same frequency traveling in the same direction simultaneously, the phenomenon of intensity of resultant waves incoming maximum and minimum is called of interference. (ii)Equation of resultant waves formed by superposition of two waves: y 1 = a 1 Sin ( wt +  ) and y 2 = Sin ( wt + ) will be y = y 1 + y 2 = A Sin ( wt + ) Amplitude of the resultant wave  (iii) Intensity of the resultant wave I  A 2 or  I 1 and I 2 are seprate intensities of the superposing waves. (iv)Low of conservation of energy is ofeyed in interference also ,only the energy of the medium is redistributed. 8. Constructive and destructive interference :(i) When superposing waves are in the same phase:  the amplitude of the resultant wave A = A max = (a 1 + a 2) In this condition the interference is called ' constructive interference.'
(ii) For  is zero or a even multiple of  , where n = 0, 1, 2, 3, ......, or path difference of waves.
 , n = 0, 1, 2, ............
(iii) Then in above condition, the intersity of resultant wave is maximum.
(iv) If the interfering waves are in opposite phase then  , and path difference
 , where n = 1, 2, 3, .............
In this condition the amplitude of the resultant wave
Amin = (a 1 - a 2)
Amin = 0
(if a 1 = a 2)
Interference of this kind is called the 'destructive interference 'I in this condition the resultant intensity is also minimum.
(v) Ratio of maximum intensity and minimum intensity of a wave is
(vi)To observe clear interference of;
(a)Phase difference of the waves must the fixed.
(b) Amplitudes of the waves must the equal.
9. Beats:
(i) When two progressive sound waves of nearly equal frequencies superpose while traveling in the same direction, then the intensity of the resultant sound increased and decreased with time.
(ii) The increased and decreased (waxing and waning) of intensity of sound occurs with a regular Interval. This regular (maxing and waning of sound is called beats. One decrease and one increase together make one BEAT.
(iii) Number of heats produces in one same to the heat frequency
(iv) If the frequencies of the waves are m and n (m > n),then heat frequency = m - n. This difference must not be greater than 10Hz, otherwise beats are not heard.
(v) Beat period = 
(vi) If the waves producing beats are
y1 = a1 sin 2 nt
and y2 = a2 sin 2mt,
then the equation of the resultant wave is
y = y1 + y2 = A sin 2(m - n)t
and the amplitude of wave is
10.Applicateins of heats ;
1.In the tuning of radio receiver .
2.In manufacturing the of and stable f
3.Indetecting poisonous gases produced in mines .
4.In the tuning of musical instruments.
5.Indetermining unknown frequency of tuning fork ;Let the known frequency the of tuning fork be unknown frequency be n and the n number .of heats produced be N while playing these two together .
a. If by putting lone wax on the arm of unknown frequency tuning fork ;
if the beat frequency decreases then n = m + N
if the beat frequency increases ,then n = m - N
b. If by putting wax on the arm of known frequency tuning fork .
if the heat frequency decreases then n = m - N
if the heat frequency increases then n = m + N
C. If the arm of unknown frequency luring fork are filed then .
if the heat frequency increase n = m + N
if the heat frequency decrease n = m - N
11. Refection of sound waves when a wave passes from one medium to the other:
a. Reflection from a rigid wall as a denser medium:
1. phase change of
3.no change in the nature of wave .
4.compression is reflected as compression and rarefaction as a rarefaction .
5.node is always formed at rigid surface .
6.direction of wave is changed .
b. reflection from rarer medium.
1. no change in the phase .
2. no change in the path difference
3. no change in the nature of wave .
4. compression is reflected as rarefaction while rarefaction as compression .
5. antinode is formed at the surface of a rare medium .
6, direction of the wave is charged .
12. Stationary wave :
(i) This is the wave produced by the superposition of two identical waves travelling along the same straight line but in opposite direction.
(ii) Energy is not transferred by these waves in the medium. It is only redictributed.
(iii) If y1 = a sin (wt - kx) be the prograssive wave along +ve x - axis and y 2 = a sin (wt + kx) be the progressive wave along -ve x - axis, then for the resultant stationary wave.
y = y1 + y2 = [2a cos kx] sin wt
(iv) Its amplitude is A = 2a cos kx = 2a cos this depends on position x.
(v) Antinodes: At these points the amplitude if the vibrating particles is maximum (A = Amax),
Amax = a1 + a2, and the change in pressure and the density is mimimum.
|
