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An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is :
- a)31.25
- b)62.50
- c)93.75
- d)125
Correct answer is option 'A,C'. Can you explain this answer?
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Verified Answer
An air column in a pipe, which is closed at one end, will be in resona...
The wavelengths possible in an air column in a pipe which has one closed end is
n = 264 Hz as it is in resonance with a vibrating turning fork of frequency 264 Hz.
Most Upvoted Answer
An air column in a pipe, which is closed at one end, will be in resona...
Given:
Frequency of tuning fork = 264 Hz
To find:
Length of the air column in cm
Formula:
The formula for the resonance of an air column in a closed pipe is given by:
L = (n * λ) / 4
Where:
L is the length of the air column
n is the harmonic number (1, 2, 3, ...)
λ is the wavelength of the sound wave
Solution:
1. Determine the wavelength of the sound wave.
The wavelength of a sound wave can be calculated using the formula:
λ = v / f
Where:
λ is the wavelength
v is the speed of sound in air
f is the frequency of the sound wave
The speed of sound in air is approximately 343 m/s.
λ = 343 m/s / 264 Hz
λ ≈ 1.298 m
2. Determine the length of the air column.
Since the pipe is closed at one end, the fundamental frequency (n = 1) will produce a quarter of a wavelength within the length of the pipe.
L = (1 * λ) / 4
L = 1.298 m / 4
L ≈ 0.3245 m
To convert the length to centimeters, multiply by 100:
L ≈ 0.3245 m * 100 cm/m
L ≈ 32.45 cm
Therefore, the length of the air column in cm is approximately 32.45 cm.
Now let's check the given options:
a) 31.25 cm: Not equal to the calculated length
b) 62.50 cm: Not equal to the calculated length
c) 93.75 cm: Not equal to the calculated length
d) 125 cm: Not equal to the calculated length
Therefore, the correct answers are options A and C, which correspond to a length of approximately 31.25 cm and 93.75 cm, respectively.
Frequency of tuning fork = 264 Hz
To find:
Length of the air column in cm
Formula:
The formula for the resonance of an air column in a closed pipe is given by:
L = (n * λ) / 4
Where:
L is the length of the air column
n is the harmonic number (1, 2, 3, ...)
λ is the wavelength of the sound wave
Solution:
1. Determine the wavelength of the sound wave.
The wavelength of a sound wave can be calculated using the formula:
λ = v / f
Where:
λ is the wavelength
v is the speed of sound in air
f is the frequency of the sound wave
The speed of sound in air is approximately 343 m/s.
λ = 343 m/s / 264 Hz
λ ≈ 1.298 m
2. Determine the length of the air column.
Since the pipe is closed at one end, the fundamental frequency (n = 1) will produce a quarter of a wavelength within the length of the pipe.
L = (1 * λ) / 4
L = 1.298 m / 4
L ≈ 0.3245 m
To convert the length to centimeters, multiply by 100:
L ≈ 0.3245 m * 100 cm/m
L ≈ 32.45 cm
Therefore, the length of the air column in cm is approximately 32.45 cm.
Now let's check the given options:
a) 31.25 cm: Not equal to the calculated length
b) 62.50 cm: Not equal to the calculated length
c) 93.75 cm: Not equal to the calculated length
d) 125 cm: Not equal to the calculated length
Therefore, the correct answers are options A and C, which correspond to a length of approximately 31.25 cm and 93.75 cm, respectively.
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An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is :a)31.25b)62.50c)93.75d)125Correct answer is option 'A,C'. Can you explain this answer?
Question Description
An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is :a)31.25b)62.50c)93.75d)125Correct answer is option 'A,C'. 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 air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is :a)31.25b)62.50c)93.75d)125Correct answer is option 'A,C'. 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 air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is :a)31.25b)62.50c)93.75d)125Correct answer is option 'A,C'. Can you explain this answer?.
An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is :a)31.25b)62.50c)93.75d)125Correct answer is option 'A,C'. 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 air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is :a)31.25b)62.50c)93.75d)125Correct answer is option 'A,C'. 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 air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is :a)31.25b)62.50c)93.75d)125Correct answer is option 'A,C'. Can you explain this answer?.
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An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is :a)31.25b)62.50c)93.75d)125Correct answer is option 'A,C'. Can you explain this answer?, a detailed solution for An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is :a)31.25b)62.50c)93.75d)125Correct answer is option 'A,C'. Can you explain this answer? has been provided alongside types of An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency 264 Hz if the length of the column in cm is :a)31.25b)62.50c)93.75d)125Correct answer is option 'A,C'. Can you explain this answer? theory, EduRev gives you an
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