JEE Exam > JEE Questions > Two oscillators ar e started simultaneously i...
Start Learning for Free
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?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
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%.
Free Test
FREE
| Start Free Test |
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.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
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?
Question Description
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?.
Solutions 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? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning 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? defined & explained in the simplest way possible. Besides giving the explanation 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?, 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
ample number of questions to practice 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? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup