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A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP in 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.
Correct answer is '106'. Can you explain this answer?
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A one metre long (both ends open) organ pipe is kept in a gas that has...
Frequency of the fundamental mode of vibration in an open organ pipe can be given by the formula:
f1 = (v / 2L)
where f1 is the frequency of the fundamental mode, v is the speed of sound, and L is the length of the pipe.
Similarly, the frequency of the second harmonic can be given by:
f2 = (2v / 2L) = (v / L)
Given that the length of the pipe is 1 meter and the speed of sound in air at STP is 300 m/s, we can calculate the frequencies as follows:
f1 = (300 / 2*1) = 150 Hz
f2 = (300 / 1) = 300 Hz
The frequency difference between the fundamental and second harmonic is given by:
Δf = f2 - f1
Substituting the values, we get:
Δf = 300 - 150 = 150 Hz
However, in this case, the organ pipe is not in air, but in a gas that has double the density of air at STP. Since the speed of sound is inversely proportional to the square root of the density of the medium, the speed of sound in this gas would be:
v' = v / sqrt(2)
Using this new speed of sound, we can calculate the frequencies as follows:
f1' = (v' / 2L) = (v / sqrt(2)) / 2L = (300 / sqrt(2)) / 2*1 = 106.07 Hz
f2' = (v' / L) = (v / sqrt(2)) / L = (300 / sqrt(2)) / 1 = 212.14 Hz
The frequency difference between the fundamental and second harmonic in this case is:
Δf' = f2' - f1' = 212.14 - 106.07 = 106.07 Hz
Therefore, the correct answer is 106 Hz.
f1 = (v / 2L)
where f1 is the frequency of the fundamental mode, v is the speed of sound, and L is the length of the pipe.
Similarly, the frequency of the second harmonic can be given by:
f2 = (2v / 2L) = (v / L)
Given that the length of the pipe is 1 meter and the speed of sound in air at STP is 300 m/s, we can calculate the frequencies as follows:
f1 = (300 / 2*1) = 150 Hz
f2 = (300 / 1) = 300 Hz
The frequency difference between the fundamental and second harmonic is given by:
Δf = f2 - f1
Substituting the values, we get:
Δf = 300 - 150 = 150 Hz
However, in this case, the organ pipe is not in air, but in a gas that has double the density of air at STP. Since the speed of sound is inversely proportional to the square root of the density of the medium, the speed of sound in this gas would be:
v' = v / sqrt(2)
Using this new speed of sound, we can calculate the frequencies as follows:
f1' = (v' / 2L) = (v / sqrt(2)) / 2L = (300 / sqrt(2)) / 2*1 = 106.07 Hz
f2' = (v' / L) = (v / sqrt(2)) / L = (300 / sqrt(2)) / 1 = 212.14 Hz
The frequency difference between the fundamental and second harmonic in this case is:
Δf' = f2' - f1' = 212.14 - 106.07 = 106.07 Hz
Therefore, the correct answer is 106 Hz.
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A one metre long (both ends open) organ pipe is kept in a gas that has...
vair = 300 m/s
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A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP in 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.Correct answer is '106'. Can you explain this answer?
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A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP in 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.Correct answer is '106'. 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 A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP in 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.Correct answer is '106'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP in 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.Correct answer is '106'. Can you explain this answer?.
A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP in 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.Correct answer is '106'. 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 A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP in 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.Correct answer is '106'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP in 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.Correct answer is '106'. Can you explain this answer?.
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A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP in 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.Correct answer is '106'. Can you explain this answer?, a detailed solution for A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP in 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.Correct answer is '106'. Can you explain this answer? has been provided alongside types of A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP in 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.Correct answer is '106'. Can you explain this answer? theory, EduRev gives you an
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