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A sinusoidal wave is propagating in negative x–direction in a string stretched along x-axis. A  particle of string at  x = 2m  is found at its mean position and it is moving in positive y direction at t = 1 sec. The amplitude of the wave, the wavelength and the angular frequency of the wave are 0.1meter, π/4 meter and 4π rad/sec respectively.
Q. The equation of the wave is :
  • a)
    y = 0.1 sin [4p(t –1)+ 8(x – 2)]
  • b)
    y = 0.1 sin [(t–1)– (x – 2)]
  • c)
    y = 0.1 sin [4p(t –1)–8(x – 2)]    
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A sinusoidal wave is propagating in negative x–direction in a st...
The equation of wave moving in negative x-direction, assuming origin of position at x = 2 and origin of time (i.e. initial time) at t = 1 sec.
Shifting the origin of position to left by 2m, that is, to x = 0. Also shifting the origin of time backwards by 1 sec, that
is to t = 0 sec. 
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Most Upvoted Answer
A sinusoidal wave is propagating in negative x–direction in a st...
Given Information:
- Amplitude (A) = 0.1 m
- Wavelength (λ) = π/4 m
- Angular frequency (ω) = 4π rad/sec
- Particle at x = 2m is at mean position at t = 1 sec

Equation of a Sinusoidal Wave:
The general equation of a sinusoidal wave traveling in the negative x-direction is given by:
y = A sin(kx - ωt + φ)

Identifying Parameters:
- Amplitude (A) = 0.1
- Wavelength (λ) = 2π/k = π/4
- Angular frequency (ω) = 4π
- Phase constant (φ) = 0 (particle at mean position)

Finding the Wave Number (k):
From the wavelength formula, λ = 2π/k, we find k = 8

Substitute Values:
Now, substituting the given values into the general equation:
y = 0.1 sin(8x - 4πt)

Adjusting for Particle's Position at t = 1 sec:
When t = 1 sec, x = 2m, the particle is at its mean position.
Substitute x = 2, t = 1 into the equation:
y = 0.1 sin(8(2) - 4π(1)) = 0.1 sin(16 - 4π) = 0.1 sin(8π - 4π) = 0.1 sin(4π)

Final Equation:
y = 0.1 sin(4π(t - 1) + 8(x - 2))
Therefore, the correct equation of the wave is:
y = 0.1 sin[4π(t - 1) + 8(x - 2)] (Option A)
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A sinusoidal wave is propagating in negative x–direction in a string stretched along x-axis. A particle of string at x = 2m is found at its mean position and it is moving in positive y direction at t = 1 sec. The amplitude of the wave, the wavelength and the angular frequency of the wave are 0.1meter, π/4 meter and 4π rad/sec respectively.Q.The equation of the wave is :a)y = 0.1 sin [4p(t –1)+ 8(x – 2)]b)y = 0.1 sin [(t–1)– (x – 2)]c)y = 0.1 sin [4p(t –1)–8(x – 2)] d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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A sinusoidal wave is propagating in negative x–direction in a string stretched along x-axis. A particle of string at x = 2m is found at its mean position and it is moving in positive y direction at t = 1 sec. The amplitude of the wave, the wavelength and the angular frequency of the wave are 0.1meter, π/4 meter and 4π rad/sec respectively.Q.The equation of the wave is :a)y = 0.1 sin [4p(t –1)+ 8(x – 2)]b)y = 0.1 sin [(t–1)– (x – 2)]c)y = 0.1 sin [4p(t –1)–8(x – 2)] d)None of theseCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A sinusoidal wave is propagating in negative x–direction in a string stretched along x-axis. A particle of string at x = 2m is found at its mean position and it is moving in positive y direction at t = 1 sec. The amplitude of the wave, the wavelength and the angular frequency of the wave are 0.1meter, π/4 meter and 4π rad/sec respectively.Q.The equation of the wave is :a)y = 0.1 sin [4p(t –1)+ 8(x – 2)]b)y = 0.1 sin [(t–1)– (x – 2)]c)y = 0.1 sin [4p(t –1)–8(x – 2)] d)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sinusoidal wave is propagating in negative x–direction in a string stretched along x-axis. A particle of string at x = 2m is found at its mean position and it is moving in positive y direction at t = 1 sec. The amplitude of the wave, the wavelength and the angular frequency of the wave are 0.1meter, π/4 meter and 4π rad/sec respectively.Q.The equation of the wave is :a)y = 0.1 sin [4p(t –1)+ 8(x – 2)]b)y = 0.1 sin [(t–1)– (x – 2)]c)y = 0.1 sin [4p(t –1)–8(x – 2)] d)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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