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An organ pipe, open from both end produces 5 beats per second when vibrated with a source of frequency 200 Hz. The second harmonic of the same pipes produces 10 beats per second with a source of frequency 420 Hz. The fundamental frequency of organ pipe is
- a)195 Hz
- b)205 Hz
- c)190 Hz
- d)210 Hz
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
An organ pipe, open from both end produces 5 beats per second when vib...
Let the fundamental frequency of organ pipe be f
Case I : f = 200 ± 5 = 205 Hz or 195 Hz
Case II : frequency of 2nd harmonic of organ pipe = 2f (as is clear from the second figure) 2f = 420 ± 10 or f = 210 ± 5 or f = 205 or 215
Hence fundamental frequency of organ pipe = 205 Hz
Case I : f = 200 ± 5 = 205 Hz or 195 Hz
Case II : frequency of 2nd harmonic of organ pipe = 2f (as is clear from the second figure) 2f = 420 ± 10 or f = 210 ± 5 or f = 205 or 215
Hence fundamental frequency of organ pipe = 205 Hz
Most Upvoted Answer
An organ pipe, open from both end produces 5 beats per second when vib...
Given:
Frequency of source for producing 5 beats per second, f1 = 200 Hz
Frequency of source for producing 10 beats per second, f2 = 420 Hz
To find:
Fundamental frequency of the organ pipe, f0
Solution:
When an organ pipe is vibrated with a source of frequency f, it produces a fundamental frequency f0 and harmonics n*f0.
Let the length of the pipe be l.
For an open pipe, the fundamental frequency can be given as:
f0 = v/2l ----(1)
where v is the speed of sound in air.
For a pipe open at both ends, the harmonics can be given as:
fn = n*v/2l ----(2)
Let's find the beat frequency for the fundamental frequency:
Beat frequency = |f1 - f0| = 5 Hz
Substituting f0 from equation (1), we get:
5 = |200 - v/2l|
Since the pipe is open at both ends, we can use equation (2) to find the length of the pipe for the second harmonic:
420 = 2*v/l
=> l = 2*v/420 = v/210
Substituting the value of l in the beat frequency equation, we get:
5 = |200 - v/2(v/210)|
=> 5 = |200 - 105|
=> v = 205 m/s
Substituting the value of v in equation (1), we get:
f0 = 205/2l = 205/2(v/210) = 210 Hz
Therefore, the fundamental frequency of the organ pipe is 210 Hz.
Frequency of source for producing 5 beats per second, f1 = 200 Hz
Frequency of source for producing 10 beats per second, f2 = 420 Hz
To find:
Fundamental frequency of the organ pipe, f0
Solution:
When an organ pipe is vibrated with a source of frequency f, it produces a fundamental frequency f0 and harmonics n*f0.
Let the length of the pipe be l.
For an open pipe, the fundamental frequency can be given as:
f0 = v/2l ----(1)
where v is the speed of sound in air.
For a pipe open at both ends, the harmonics can be given as:
fn = n*v/2l ----(2)
Let's find the beat frequency for the fundamental frequency:
Beat frequency = |f1 - f0| = 5 Hz
Substituting f0 from equation (1), we get:
5 = |200 - v/2l|
Since the pipe is open at both ends, we can use equation (2) to find the length of the pipe for the second harmonic:
420 = 2*v/l
=> l = 2*v/420 = v/210
Substituting the value of l in the beat frequency equation, we get:
5 = |200 - v/2(v/210)|
=> 5 = |200 - 105|
=> v = 205 m/s
Substituting the value of v in equation (1), we get:
f0 = 205/2l = 205/2(v/210) = 210 Hz
Therefore, the fundamental frequency of the organ pipe is 210 Hz.
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An organ pipe, open from both end produces 5 beats per second when vibrated with a source of frequency 200 Hz. The second harmonic of the same pipes produces 10 beats per second with a source of frequency 420 Hz. The fundamental frequency of organ pipe isa)195 Hzb)205 Hzc)190 Hzd)210 HzCorrect answer is option 'B'. Can you explain this answer?
Question Description
An organ pipe, open from both end produces 5 beats per second when vibrated with a source of frequency 200 Hz. The second harmonic of the same pipes produces 10 beats per second with a source of frequency 420 Hz. The fundamental frequency of organ pipe isa)195 Hzb)205 Hzc)190 Hzd)210 HzCorrect 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 An organ pipe, open from both end produces 5 beats per second when vibrated with a source of frequency 200 Hz. The second harmonic of the same pipes produces 10 beats per second with a source of frequency 420 Hz. The fundamental frequency of organ pipe isa)195 Hzb)205 Hzc)190 Hzd)210 HzCorrect 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 An organ pipe, open from both end produces 5 beats per second when vibrated with a source of frequency 200 Hz. The second harmonic of the same pipes produces 10 beats per second with a source of frequency 420 Hz. The fundamental frequency of organ pipe isa)195 Hzb)205 Hzc)190 Hzd)210 HzCorrect answer is option 'B'. Can you explain this answer?.
An organ pipe, open from both end produces 5 beats per second when vibrated with a source of frequency 200 Hz. The second harmonic of the same pipes produces 10 beats per second with a source of frequency 420 Hz. The fundamental frequency of organ pipe isa)195 Hzb)205 Hzc)190 Hzd)210 HzCorrect 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 An organ pipe, open from both end produces 5 beats per second when vibrated with a source of frequency 200 Hz. The second harmonic of the same pipes produces 10 beats per second with a source of frequency 420 Hz. The fundamental frequency of organ pipe isa)195 Hzb)205 Hzc)190 Hzd)210 HzCorrect 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 An organ pipe, open from both end produces 5 beats per second when vibrated with a source of frequency 200 Hz. The second harmonic of the same pipes produces 10 beats per second with a source of frequency 420 Hz. The fundamental frequency of organ pipe isa)195 Hzb)205 Hzc)190 Hzd)210 HzCorrect answer is option 'B'. Can you explain this answer?.
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