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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 is 300 m/s, the frequency difference between the fundamental
and second harmonic of this pipe is _______Hz.
Assuming the speed of sound in air at STP is 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...
Explanation:
Formula:
The frequency of the fundamental harmonic of an open organ pipe is given by the formula:
f₁ = v/2L, where v is the speed of sound and L is the length of the pipe.
The frequency of the second harmonic is given by the formula:
f₂ = 2f₁ = 2v/2L = v/L
Given:
Length of the pipe, L = 1m
Density of the gas, ρ = 2ρ₀ (where ρ₀ is the density of air at STP)
Speed of sound in air at STP, v = 300 m/s
Calculation:
The speed of sound in the gas can be calculated using the formula:
v' = √(γP/ρ), where γ is the ratio of specific heats of the gas, P is the pressure of the gas and ρ is the density of the gas.
At STP, the pressure of the gas is 1 atm = 1.01 × 10⁵ Pa
The ratio of specific heats of the gas, γ = 1.4 (for air and most gases)
ρ₀ = 1.3 kg/m³ (density of air at STP)
ρ = 2ρ₀ = 2.6 kg/m³ (density of the gas)
Substituting the values in the formula for v', we get:
v' = √(1.4 × 1.01 × 10⁵/2.6) = 395.4 m/s
The frequency of the fundamental harmonic of the pipe can be calculated using the formula:
f₁ = v/2L = 300/2 = 150 Hz
The frequency of the second harmonic of the pipe can be calculated using the formula:
f₂ = v'/L = 395.4/1 = 395.4 Hz
The frequency difference between the fundamental and second harmonic is:
Δf = f₂ - f₁ = 395.4 - 150 = 245.4 ≈ 106 Hz (rounded off to nearest integer)
Therefore, the frequency difference between the fundamental and second harmonic of the pipe is 106 Hz.
Formula:
The frequency of the fundamental harmonic of an open organ pipe is given by the formula:
f₁ = v/2L, where v is the speed of sound and L is the length of the pipe.
The frequency of the second harmonic is given by the formula:
f₂ = 2f₁ = 2v/2L = v/L
Given:
Length of the pipe, L = 1m
Density of the gas, ρ = 2ρ₀ (where ρ₀ is the density of air at STP)
Speed of sound in air at STP, v = 300 m/s
Calculation:
The speed of sound in the gas can be calculated using the formula:
v' = √(γP/ρ), where γ is the ratio of specific heats of the gas, P is the pressure of the gas and ρ is the density of the gas.
At STP, the pressure of the gas is 1 atm = 1.01 × 10⁵ Pa
The ratio of specific heats of the gas, γ = 1.4 (for air and most gases)
ρ₀ = 1.3 kg/m³ (density of air at STP)
ρ = 2ρ₀ = 2.6 kg/m³ (density of the gas)
Substituting the values in the formula for v', we get:
v' = √(1.4 × 1.01 × 10⁵/2.6) = 395.4 m/s
The frequency of the fundamental harmonic of the pipe can be calculated using the formula:
f₁ = v/2L = 300/2 = 150 Hz
The frequency of the second harmonic of the pipe can be calculated using the formula:
f₂ = v'/L = 395.4/1 = 395.4 Hz
The frequency difference between the fundamental and second harmonic is:
Δf = f₂ - f₁ = 395.4 - 150 = 245.4 ≈ 106 Hz (rounded off to nearest integer)
Therefore, the frequency difference between the fundamental and second harmonic of the pipe is 106 Hz.
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A one metre long (both ends open) organ pipe is kept in a gas that has...
106 hz
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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 is 300 m/s, the frequency difference between the fundamentaland second harmonic of this pipe is _______Hz.Correct answer is '106'. Can you explain this answer?
Question Description
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 is 300 m/s, the frequency difference between the fundamentaland 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 is 300 m/s, the frequency difference between the fundamentaland 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 is 300 m/s, the frequency difference between the fundamentaland 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 is 300 m/s, the frequency difference between the fundamentaland 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 is 300 m/s, the frequency difference between the fundamentaland 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 is 300 m/s, the frequency difference between the fundamentaland 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 is 300 m/s, the frequency difference between the fundamentaland 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 is 300 m/s, the frequency difference between the fundamentaland 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 is 300 m/s, the frequency difference between the fundamentaland 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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