At a certain point two waves create pressure variations as p1 = P sin (2π νt) and p2 = P sin 2π(νt - φ), Amplitude of resultant wave at this point when φ = 1/4 is  

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  1. 2P
  2. P
  3. P\(\sqrt{2}\,\)
  4. 0

Answer (Detailed Solution Below)

Option 4 : 0
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Amplitude of resultant wave will be the summation of given two waves which can be given as:

∴ Ptotal = P+ P2

∴ Ptotal = P sin (2π vt) + P sin 2π(vt - ϕ )

∴ Ptotal = P [ sin (2π vt) + P sin 2π(vt - ϕ)]

∴ Ptotal = P [ 2 cos( \(\frac{2π vt + 2π(vt-ϕ)}{2}\)) sin (\(\frac{2π vt -2π(vt-ϕ)}{2}\))]

∴ Ptotal = P [ 2 cos (πϕ) ⋅ sin (ϕπ) ]

∴ Ptotal = P [ sin (2πϕ)]

∴ Ptotal = P (0)

∴ Ptotal = 0

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