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Two oscillators ar e started simultaneously in same phase. After 50 oscillations of one, they get out of phase by p, that is half oscillation. The percentage difference of frequencies of the two oscillators is nearest to
- a)2%
- b)1%
- c)0.5%
- d)0.25%
Correct answer is option 'B'. Can you explain this answer?
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Two oscillators ar e started simultaneously in same phase. After 50 os...
Problem: Two oscillators are started simultaneously in the same phase. After 50 oscillations of one, they get out of phase by p, that is half oscillation. The percentage difference of frequencies of the two oscillators is nearest to:
Solution:
Let the frequencies of the two oscillators be f1 and f2.
Initial phase difference = 0
Phase difference after 50 oscillations of one = p = π
Method 1:
We know that the phase difference between two oscillators is given by:
Phase difference = 2π(f1 - f2)t ----(1)
where t is the time interval.
From the given information, we have:
50 oscillations of one = 50/f1 seconds
Phase difference = π radians
Substituting these values in equation (1), we get:
π = 2π(f1 - f2)(50/f1)
Simplifying, we get:
f1 - f2 = 1/100
Percentage difference of frequencies = (|f1 - f2|/[(f1+f2)/2]) x 100
Substituting the value of f1 - f2, we get:
Percentage difference of frequencies = (1/100)/[(f1+f2)/2] x 100
= 1% (approx)
Therefore, the nearest answer is option B, 1%.
Method 2:
We can also solve this problem using the concept of beats. Beats are produced when two sound waves of slightly different frequencies interfere with each other. The beat frequency is equal to the difference between the frequencies of the two sound waves.
In this case, the two oscillators produce beats with a frequency of 1/100 Hz. Therefore, the frequency of one oscillator is slightly higher than the other by 1/200 Hz (half of the beat frequency).
Percentage difference of frequencies = (1/200)/[(f1+f2)/2] x 100
= 0.5% (approx)
Therefore, the nearest answer is option B, 1%.
Solution:
Let the frequencies of the two oscillators be f1 and f2.
Initial phase difference = 0
Phase difference after 50 oscillations of one = p = π
Method 1:
We know that the phase difference between two oscillators is given by:
Phase difference = 2π(f1 - f2)t ----(1)
where t is the time interval.
From the given information, we have:
50 oscillations of one = 50/f1 seconds
Phase difference = π radians
Substituting these values in equation (1), we get:
π = 2π(f1 - f2)(50/f1)
Simplifying, we get:
f1 - f2 = 1/100
Percentage difference of frequencies = (|f1 - f2|/[(f1+f2)/2]) x 100
Substituting the value of f1 - f2, we get:
Percentage difference of frequencies = (1/100)/[(f1+f2)/2] x 100
= 1% (approx)
Therefore, the nearest answer is option B, 1%.
Method 2:
We can also solve this problem using the concept of beats. Beats are produced when two sound waves of slightly different frequencies interfere with each other. The beat frequency is equal to the difference between the frequencies of the two sound waves.
In this case, the two oscillators produce beats with a frequency of 1/100 Hz. Therefore, the frequency of one oscillator is slightly higher than the other by 1/200 Hz (half of the beat frequency).
Percentage difference of frequencies = (1/200)/[(f1+f2)/2] x 100
= 0.5% (approx)
Therefore, the nearest answer is option B, 1%.
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Community Answer
Two oscillators ar e started simultaneously in same phase. After 50 os...
Phase change π in 50 oscillations.
Phase change 2π in 100 oscillations.
So frequency different ~ 1 in 100.
Phase change 2π in 100 oscillations.
So frequency different ~ 1 in 100.
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Two oscillators ar e started simultaneously in same phase. After 50 oscillations of one, they get out of phase by p, that is half oscillation. The percentage difference of frequencies of the two oscillators is nearest toa)2%b)1%c)0.5%d)0.25%Correct answer is option 'B'. Can you explain this answer?
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Two oscillators ar e started simultaneously in same phase. After 50 oscillations of one, they get out of phase by p, that is half oscillation. The percentage difference of frequencies of the two oscillators is nearest toa)2%b)1%c)0.5%d)0.25%Correct answer is option 'B'. 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 Two oscillators ar e started simultaneously in same phase. After 50 oscillations of one, they get out of phase by p, that is half oscillation. The percentage difference of frequencies of the two oscillators is nearest toa)2%b)1%c)0.5%d)0.25%Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two oscillators ar e started simultaneously in same phase. After 50 oscillations of one, they get out of phase by p, that is half oscillation. The percentage difference of frequencies of the two oscillators is nearest toa)2%b)1%c)0.5%d)0.25%Correct answer is option 'B'. Can you explain this answer?.
Two oscillators ar e started simultaneously in same phase. After 50 oscillations of one, they get out of phase by p, that is half oscillation. The percentage difference of frequencies of the two oscillators is nearest toa)2%b)1%c)0.5%d)0.25%Correct answer is option 'B'. 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 Two oscillators ar e started simultaneously in same phase. After 50 oscillations of one, they get out of phase by p, that is half oscillation. The percentage difference of frequencies of the two oscillators is nearest toa)2%b)1%c)0.5%d)0.25%Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two oscillators ar e started simultaneously in same phase. After 50 oscillations of one, they get out of phase by p, that is half oscillation. The percentage difference of frequencies of the two oscillators is nearest toa)2%b)1%c)0.5%d)0.25%Correct answer is option 'B'. Can you explain this answer?.
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Two oscillators ar e started simultaneously in same phase. After 50 oscillations of one, they get out of phase by p, that is half oscillation. The percentage difference of frequencies of the two oscillators is nearest toa)2%b)1%c)0.5%d)0.25%Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Two oscillators ar e started simultaneously in same phase. After 50 oscillations of one, they get out of phase by p, that is half oscillation. The percentage difference of frequencies of the two oscillators is nearest toa)2%b)1%c)0.5%d)0.25%Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Two oscillators ar e started simultaneously in same phase. After 50 oscillations of one, they get out of phase by p, that is half oscillation. The percentage difference of frequencies of the two oscillators is nearest toa)2%b)1%c)0.5%d)0.25%Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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