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A plane sound wave is travelling in a medium. In a reference frame A fixed  to the medium , its equation is  y = a cos(ωt − kx ) . With respect to reference frame B, moving with a constant velocity v in the direction of propagation of the wave, equation of the wave will be 
  • a)
    y = a cos[(ωt + kv) t − kx ]
  • b)
    y = −a cos[(ωt − kv) t − kx ]
  • c)
    y = a cos[(ωt − kv) t − kx ]
  • d)
    y = a cos[(ωt + kv) t + kx ]
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A plane sound wave is travelling in a medium. In a reference frame A f...
Suppose at an instant t, the x – coordinate of a point with reference to moving frame is x0. Since at this moment, origin of moving frame is at distance vt from origin of the fixed reference frame, therefore, putting this value of x in the given equation, we get
y = a cos[ωt − k (vt − x )]
y = a cos[(ωt − kv)t − kx ]
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Most Upvoted Answer
A plane sound wave is travelling in a medium. In a reference frame A f...
Explanation:

Given: Equation of the wave in reference frame A: y = a cos(ωt - kx)

Transformation from A to B:
- Reference frame B is moving with a constant velocity v in the direction of propagation of the wave.
- The transformation from A to B involves replacing t with (t + x/v) in the equation of the wave.

Equation of the wave in reference frame B:
- Substituting t with (t + x/v) in the equation of the wave in reference frame A:
y = a cos(ω(t + x/v) - kx)
y = a cos(ωt + ωx/v - kx)
y = a cos[(ωt - kv) - kx]
y = a cos[(ωt - kv)t - kx] (Option C)
Therefore, the correct equation of the wave in reference frame B would be y = a cos[(ωt - kv)t - kx].
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A plane sound wave is travelling in a medium. In a reference frame A fixed to the medium , its equation is y = a cos(ωt − kx ) . With respect to reference frame B, moving with a constant velocity v in the direction of propagation of the wave, equation of the wave will bea)y = a cos[(ωt + kv) t − kx ]b)y = −a cos[(ωt − kv) t − kx ]c)y = a cos[(ωt − kv) t − kx ]d)y = a cos[(ωt + kv) t + kx ]Correct answer is option 'C'. Can you explain this answer?
Question Description
A plane sound wave is travelling in a medium. In a reference frame A fixed to the medium , its equation is y = a cos(ωt − kx ) . With respect to reference frame B, moving with a constant velocity v in the direction of propagation of the wave, equation of the wave will bea)y = a cos[(ωt + kv) t − kx ]b)y = −a cos[(ωt − kv) t − kx ]c)y = a cos[(ωt − kv) t − kx ]d)y = a cos[(ωt + kv) t + kx ]Correct answer is option 'C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A plane sound wave is travelling in a medium. In a reference frame A fixed to the medium , its equation is y = a cos(ωt − kx ) . With respect to reference frame B, moving with a constant velocity v in the direction of propagation of the wave, equation of the wave will bea)y = a cos[(ωt + kv) t − kx ]b)y = −a cos[(ωt − kv) t − kx ]c)y = a cos[(ωt − kv) t − kx ]d)y = a cos[(ωt + kv) t + kx ]Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A plane sound wave is travelling in a medium. In a reference frame A fixed to the medium , its equation is y = a cos(ωt − kx ) . With respect to reference frame B, moving with a constant velocity v in the direction of propagation of the wave, equation of the wave will bea)y = a cos[(ωt + kv) t − kx ]b)y = −a cos[(ωt − kv) t − kx ]c)y = a cos[(ωt − kv) t − kx ]d)y = a cos[(ωt + kv) t + kx ]Correct answer is option 'C'. Can you explain this answer?.
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