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Question

A wave travelling along the positive xdirection having maximum displacement along ydirection as 1 m, wavelength 2π m and frequency of 1/π Hz is represented by:
  1. y=sin(2πx2πt)
  2. y=sin(10πx20πt)
  3. y=sin(x2t)
  4. y=sin(2πx+2πt)


Solution

The correct option is C y=sin(x2t)
Maximum vertical( ydirection) displacement of particle on string is the amplitude of wave
A=1 m
Wavelength(λ)=2π m,
frequency (f)=1π Hz
Let the equation of wave be,
y=Asin(kxωt+ϕ)
where k=2πλ and ω=2πf
y=1×sin(2π2πx2ππt+ϕ)
y=sin(x2t+ϕ)
Now if at time t=0, particle on string at x=0 starts motion from its mean position i.e y=0 then phase constant ϕ=0.
Hence the wave equation will reduce to,
y=sin(x2t)
Option (a) is correct.

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