Four different independent waves are represented bya y1-a1sin- 1tb y2-a2sin- 2tc y3-a3sin- 3td y4-a4sin - 4 t - - -3The sustained interference is possible due to

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Principle of Superposition

Four differen...

Question

Four different independent waves are represented by
a) $y_{1} = a_{1} sin ω_{1} t$
b) $y_{2} = a_{2} sin ω_{2} t$
c) $y_{3} = a_{3} sin ω_{3} t$
d) $y_{4} = a_{4} sin (ω_{4} t + π / 3)$
The sustained interference is possible due to

a & c

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a & d

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c & d

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Not possible with any combination

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Solution

The correct option is C Not possible with any combination
Interference takes place during the interaction of waves that have, nearly the same frequency. Four different independent waves have frequencies $w_{1}$ , $w_{2}$ , $w_{3}$ and $w_{4}$ respectively. As these frequencies are different, the interference does not take place between any combinations.
Hence, option D is correct.

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Four different independent waves are represented bya) y1=a1sinω1tb) y2=a2sinω2tc) y3=a3sinω3td) y4=a4sin(ω4t+π/3)The sustained interference is possible due to

Four different independent waves are represented by
a) $y_{1} = a_{1} sin ω_{1} t$
b) $y_{2} = a_{2} sin ω_{2} t$
c) $y_{3} = a_{3} sin ω_{3} t$
d) $y_{4} = a_{4} sin (ω_{4} t + π / 3)$
The sustained interference is possible due to