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Two sounding bodies producing progressive waves given by y1 = 4sin(400πt) and y2 = 3sin(404πt) where t is in seconds, are situated near the ears of a person. The person will hear
- a)2 beats/s with intensity ratio 4/3 between maxima and minima
- b)2 beats/s with intensity ratio 49 between maxima and minima
- c)4 beats/s with intensity ratio 49 between maxima and minima
- d)4 beats/s with intensity ratio 4/3 between maxima and minima
Correct answer is option 'B'. Can you explain this answer?
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Two sounding bodies producing progressive waves given by y1 = 4sin(400...
T) and y2 = 3sin(400t + π/3) are placed at a distance of 10 meters apart. Find the equation of the resultant wave produced by the interference of these waves.
We can use the principle of superposition to find the resultant wave. The displacement at a point due to the two waves is given by:
y = y1 + y2
y = 4sin(400t) + 3sin(400t + π/3)
Using the trigonometric identity sin(A + B) = sin(A)cos(B) + cos(A)sin(B), we can rewrite y as:
y = 4sin(400t) + 3sin(400t)cos(π/3) + 3cos(400t)sin(π/3)
y = 4sin(400t) + 3/2sin(400t) + 3sqrt(3)/2cos(400t)
y = (4 + 3/2)sin(400t) + 3sqrt(3)/2cos(400t)
y = 11/2sin(400t) + 3sqrt(3)/2cos(400t)
This is the equation of the resultant wave produced by the interference of the two waves. We can also rewrite it in the form:
y = A sin(ωt + φ)
where A = sqrt((11/2)^2 + (3sqrt(3)/2)^2) = 6.5 and φ = arctan(-3sqrt(3)/22). The angular frequency ω is 400 radians per second.
Therefore, the equation of the resultant wave is:
y = 6.5sin(400t + 1.12)
We can use the principle of superposition to find the resultant wave. The displacement at a point due to the two waves is given by:
y = y1 + y2
y = 4sin(400t) + 3sin(400t + π/3)
Using the trigonometric identity sin(A + B) = sin(A)cos(B) + cos(A)sin(B), we can rewrite y as:
y = 4sin(400t) + 3sin(400t)cos(π/3) + 3cos(400t)sin(π/3)
y = 4sin(400t) + 3/2sin(400t) + 3sqrt(3)/2cos(400t)
y = (4 + 3/2)sin(400t) + 3sqrt(3)/2cos(400t)
y = 11/2sin(400t) + 3sqrt(3)/2cos(400t)
This is the equation of the resultant wave produced by the interference of the two waves. We can also rewrite it in the form:
y = A sin(ωt + φ)
where A = sqrt((11/2)^2 + (3sqrt(3)/2)^2) = 6.5 and φ = arctan(-3sqrt(3)/22). The angular frequency ω is 400 radians per second.
Therefore, the equation of the resultant wave is:
y = 6.5sin(400t + 1.12)
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Two sounding bodies producing progressive waves given by y1 = 4sin(400πt)andy2 = 3sin(404πt)where t is in seconds, are situated near the ears of a person. The person will heara)2 beats/s with intensity ratio 4/3 betweenmaxima and minimab)2 beats/s with intensity ratio 49 between maxima and minimac)4 beats/s with intensity ratio 49 between maxima and minimad)4 beats/s with intensity ratio 4/3 betweenmaxima and minimaCorrect answer is option 'B'. Can you explain this answer?
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Two sounding bodies producing progressive waves given by y1 = 4sin(400πt)andy2 = 3sin(404πt)where t is in seconds, are situated near the ears of a person. The person will heara)2 beats/s with intensity ratio 4/3 betweenmaxima and minimab)2 beats/s with intensity ratio 49 between maxima and minimac)4 beats/s with intensity ratio 49 between maxima and minimad)4 beats/s with intensity ratio 4/3 betweenmaxima and minimaCorrect answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two sounding bodies producing progressive waves given by y1 = 4sin(400πt)andy2 = 3sin(404πt)where t is in seconds, are situated near the ears of a person. The person will heara)2 beats/s with intensity ratio 4/3 betweenmaxima and minimab)2 beats/s with intensity ratio 49 between maxima and minimac)4 beats/s with intensity ratio 49 between maxima and minimad)4 beats/s with intensity ratio 4/3 betweenmaxima and minimaCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two sounding bodies producing progressive waves given by y1 = 4sin(400πt)andy2 = 3sin(404πt)where t is in seconds, are situated near the ears of a person. The person will heara)2 beats/s with intensity ratio 4/3 betweenmaxima and minimab)2 beats/s with intensity ratio 49 between maxima and minimac)4 beats/s with intensity ratio 49 between maxima and minimad)4 beats/s with intensity ratio 4/3 betweenmaxima and minimaCorrect answer is option 'B'. Can you explain this answer?.
Two sounding bodies producing progressive waves given by y1 = 4sin(400πt)andy2 = 3sin(404πt)where t is in seconds, are situated near the ears of a person. The person will heara)2 beats/s with intensity ratio 4/3 betweenmaxima and minimab)2 beats/s with intensity ratio 49 between maxima and minimac)4 beats/s with intensity ratio 49 between maxima and minimad)4 beats/s with intensity ratio 4/3 betweenmaxima and minimaCorrect answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two sounding bodies producing progressive waves given by y1 = 4sin(400πt)andy2 = 3sin(404πt)where t is in seconds, are situated near the ears of a person. The person will heara)2 beats/s with intensity ratio 4/3 betweenmaxima and minimab)2 beats/s with intensity ratio 49 between maxima and minimac)4 beats/s with intensity ratio 49 between maxima and minimad)4 beats/s with intensity ratio 4/3 betweenmaxima and minimaCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two sounding bodies producing progressive waves given by y1 = 4sin(400πt)andy2 = 3sin(404πt)where t is in seconds, are situated near the ears of a person. The person will heara)2 beats/s with intensity ratio 4/3 betweenmaxima and minimab)2 beats/s with intensity ratio 49 between maxima and minimac)4 beats/s with intensity ratio 49 between maxima and minimad)4 beats/s with intensity ratio 4/3 betweenmaxima and minimaCorrect answer is option 'B'. Can you explain this answer?.
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