how
Constructive interference and
Destructive interference is proved by angle?
Answers
Explanation:
CONSTRUCTIVE INTERFERENCE - DEFINITION
Constructive interference: The interference of two or more waves of equal frequency and phase, resulting in their mutual reinforcement and producing a single amplitude equal to the sum of the amplitudes of the individual waves.
For Constructive interference phase difference between waves must be zero.
DESTRUCTIVE INTERFERENCE - EXAMPLE
The interference of two waves of equal frequency and opposite phase, resulting in their cancellation where the negative displacement of one always coincides with the positive displacement of the other.
Condition for destructive interference is 180 degree phase difference between superimposing waves.
USE CONDITION ON PATH DIFFERENCE FOR TWO SUPERIMPOSING SOUND WAVES FOR CONSTRUCTIVE INTERFERENCE - EXAMPLE
concept
Example: In a large room, a person receives direct sound waves from a source 120 m away from him. He also receives waves from the 25 m high ceiling at a point half way between them. For which wavelengths the two waves interfere constructively?
Solution:
Path difference is Δx
Δx=2[
25
2
+60
2
]−120=10 m
phase change δ=
λ
2π
Δx
Constructive interference for δ=2nπ, where n=1,2,3 etc.
Thus, λ
1
=10 m for n=1
λ
2
=5 m for n=2
λ
3
=10/3 m for n=3 etc.
DEFINE DESTRUCTIVE INTERFERENCE AND STATE CONDITION ON PHASE DIFFERENCE FOR DESTRUCTIVE INTERFERENCE - DEFINITION
If a crest of one wave meets a trough of another wave then the magnitude of the displacements is equal to the difference in the individual magnitudes this is known as destructive interference. For destructive interference Δx=(2n+1)
2
λ
=
2
(2n+1)
f
v
where n=1,2,.....
USE CONDITION ON PATH DIFFERENCE FOR TWO SUPERIMPOSING SOUND WAVES FOR DESTRUCTIVE INTERFERENCE - EXAMPLE
concept
Example: Two small loud speakers A and B are driven by the same amplifier as shown in figure and emit pure sinusoidal waves in phase. Speaker A is 1 m away as shown and speaker B is 2 m away from the amplifier. The microphone is 4 m away from the amplifier in transverse direction as indicated in the figure.Speed of sound is 350 m/s.
Solution:
Path difference between sound from the sources meeting at P=
4
2
+2
2
−
4
2
+1
2
=0.35m
For destructive interference, path difference=(n+
2
1
)λ=(n+
2
1
)
ν
c
(n=0,1,2,3...)
⟹ν=(n+
2
1
)
0.35
350
=1000(n+
2
1
)=500Hz,1500Hz,2500Hz.....
CONSTRUCTIVE INTERFERENCE - DEFINITION
Constructive interference occurs when the phase difference between the waves is an even multiple of (180) (a multiple of 2, 360)etc.
DESTRUCTIVE INTERFERENCE - DEFINITION
Destructive interference occurs when the difference is an odd multiple of . ... At some points, these will be in phase, and will produce a maximum displacement