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A sonometer wire is 31cm long is in resonance with a tuning fork of frequency n. If the length is
increased by 1cm and it is vibrated with the same tuning fork, then 8 beats/sec are heard. The
frequency of the tuning fork is -
increased by 1cm and it is vibrated with the same tuning fork, then 8 beats/sec are heard. The
frequency of the tuning fork is -
- a)248Hz
- b)256Hz
- c)264Hz
- d)None
Correct answer is option 'B'. Can you explain this answer?
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A sonometer wire is 31cm long is in resonance with a tuning fork of fr...
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A sonometer wire is 31cm long is in resonance with a tuning fork of fr...
Given information:
- Length of the sonometer wire in resonance with tuning fork = 31 cm
- Length of the sonometer wire when increased = 31 cm + 1 cm = 32 cm
- Beats heard when the wire is vibrated with the increased length = 8 beats/sec
Formula:
The frequency of the tuning fork can be calculated using the formula:
\(f = \frac{{v}}{{2L}}\)
Calculation:
1. Finding the frequency of the tuning fork when the wire is not increased:
Using the formula, \(f = \frac{{v}}{{2L}}\), where v is the speed of sound and L is the length of the wire.
Assuming the speed of sound is v, and the given length of the wire is 31 cm, we can calculate the frequency as:
\(f_1 = \frac{{v}}{{2 \times 31}}\)
2. Finding the frequency of the tuning fork when the wire is increased:
Using the formula, \(f = \frac{{v}}{{2L}}\), where v is the speed of sound and L is the length of the wire.
Assuming the speed of sound is v, and the given length of the wire is 32 cm, we can calculate the frequency as:
\(f_2 = \frac{{v}}{{2 \times 32}}\)
3. Finding the difference in frequency:
Since we hear 8 beats/sec when the wire is increased, the difference in frequency can be calculated as:
\(|f_1 - f_2| = 8\)
4. Solving the equations:
Substituting the values of \(f_1\) and \(f_2\) in the equation \(|f_1 - f_2| = 8\), we get:
\(\left|\frac{{v}}{{2 \times 31}} - \frac{{v}}{{2 \times 32}}\right| = 8\)
Simplifying the equation:
\(\left|\frac{{v}}{{62}} - \frac{{v}}{{64}}\right| = 8\)
Taking the LCM and simplifying further:
\(\left|\frac{{2v - v}}{{62 \times 64}}\right| = 8\)
Simplifying the equation:
\(\left|\frac{{v}}{{62 \times 64}}\right| = 8\)
Multiplying both sides by \(62 \times 64\):
\(|v| = 8 \times 62 \times 64\)
Simplifying further:
\(v = 8 \times 62 \times 64\)
5. Calculating the frequency:
Using the formula \(f = \frac{{v}}{{2L}}\), we can calculate the frequency as:
\(f = \frac{{8 \times 62 \times 64}}{{2 \times 32}}\)
Simplifying the equation:
\(f = \frac{{8 \times 62}}{{1}}\)
Calculating the value:
\(f = 8 \times 62\)
\(f = 496\)
Therefore, the frequency of the tuning fork is 496 Hz.
Conclusion:
The
- Length of the sonometer wire in resonance with tuning fork = 31 cm
- Length of the sonometer wire when increased = 31 cm + 1 cm = 32 cm
- Beats heard when the wire is vibrated with the increased length = 8 beats/sec
Formula:
The frequency of the tuning fork can be calculated using the formula:
\(f = \frac{{v}}{{2L}}\)
Calculation:
1. Finding the frequency of the tuning fork when the wire is not increased:
Using the formula, \(f = \frac{{v}}{{2L}}\), where v is the speed of sound and L is the length of the wire.
Assuming the speed of sound is v, and the given length of the wire is 31 cm, we can calculate the frequency as:
\(f_1 = \frac{{v}}{{2 \times 31}}\)
2. Finding the frequency of the tuning fork when the wire is increased:
Using the formula, \(f = \frac{{v}}{{2L}}\), where v is the speed of sound and L is the length of the wire.
Assuming the speed of sound is v, and the given length of the wire is 32 cm, we can calculate the frequency as:
\(f_2 = \frac{{v}}{{2 \times 32}}\)
3. Finding the difference in frequency:
Since we hear 8 beats/sec when the wire is increased, the difference in frequency can be calculated as:
\(|f_1 - f_2| = 8\)
4. Solving the equations:
Substituting the values of \(f_1\) and \(f_2\) in the equation \(|f_1 - f_2| = 8\), we get:
\(\left|\frac{{v}}{{2 \times 31}} - \frac{{v}}{{2 \times 32}}\right| = 8\)
Simplifying the equation:
\(\left|\frac{{v}}{{62}} - \frac{{v}}{{64}}\right| = 8\)
Taking the LCM and simplifying further:
\(\left|\frac{{2v - v}}{{62 \times 64}}\right| = 8\)
Simplifying the equation:
\(\left|\frac{{v}}{{62 \times 64}}\right| = 8\)
Multiplying both sides by \(62 \times 64\):
\(|v| = 8 \times 62 \times 64\)
Simplifying further:
\(v = 8 \times 62 \times 64\)
5. Calculating the frequency:
Using the formula \(f = \frac{{v}}{{2L}}\), we can calculate the frequency as:
\(f = \frac{{8 \times 62 \times 64}}{{2 \times 32}}\)
Simplifying the equation:
\(f = \frac{{8 \times 62}}{{1}}\)
Calculating the value:
\(f = 8 \times 62\)
\(f = 496\)
Therefore, the frequency of the tuning fork is 496 Hz.
Conclusion:
The
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A sonometer wire is 31cm long is in resonance with a tuning fork of frequency n. If the length isincreased by 1cm and it is vibrated with the same tuning fork, then 8 beats/sec are heard. Thefrequency of the tuning fork is -a)248Hzb)256Hzc)264Hzd)NoneCorrect answer is option 'B'. Can you explain this answer?
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A sonometer wire is 31cm long is in resonance with a tuning fork of frequency n. If the length isincreased by 1cm and it is vibrated with the same tuning fork, then 8 beats/sec are heard. Thefrequency of the tuning fork is -a)248Hzb)256Hzc)264Hzd)NoneCorrect 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 A sonometer wire is 31cm long is in resonance with a tuning fork of frequency n. If the length isincreased by 1cm and it is vibrated with the same tuning fork, then 8 beats/sec are heard. Thefrequency of the tuning fork is -a)248Hzb)256Hzc)264Hzd)NoneCorrect 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 A sonometer wire is 31cm long is in resonance with a tuning fork of frequency n. If the length isincreased by 1cm and it is vibrated with the same tuning fork, then 8 beats/sec are heard. Thefrequency of the tuning fork is -a)248Hzb)256Hzc)264Hzd)NoneCorrect answer is option 'B'. Can you explain this answer?.
A sonometer wire is 31cm long is in resonance with a tuning fork of frequency n. If the length isincreased by 1cm and it is vibrated with the same tuning fork, then 8 beats/sec are heard. Thefrequency of the tuning fork is -a)248Hzb)256Hzc)264Hzd)NoneCorrect 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 A sonometer wire is 31cm long is in resonance with a tuning fork of frequency n. If the length isincreased by 1cm and it is vibrated with the same tuning fork, then 8 beats/sec are heard. Thefrequency of the tuning fork is -a)248Hzb)256Hzc)264Hzd)NoneCorrect 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 A sonometer wire is 31cm long is in resonance with a tuning fork of frequency n. If the length isincreased by 1cm and it is vibrated with the same tuning fork, then 8 beats/sec are heard. Thefrequency of the tuning fork is -a)248Hzb)256Hzc)264Hzd)NoneCorrect answer is option 'B'. Can you explain this answer?.
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A sonometer wire is 31cm long is in resonance with a tuning fork of frequency n. If the length isincreased by 1cm and it is vibrated with the same tuning fork, then 8 beats/sec are heard. Thefrequency of the tuning fork is -a)248Hzb)256Hzc)264Hzd)NoneCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A sonometer wire is 31cm long is in resonance with a tuning fork of frequency n. If the length isincreased by 1cm and it is vibrated with the same tuning fork, then 8 beats/sec are heard. Thefrequency of the tuning fork is -a)248Hzb)256Hzc)264Hzd)NoneCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A sonometer wire is 31cm long is in resonance with a tuning fork of frequency n. If the length isincreased by 1cm and it is vibrated with the same tuning fork, then 8 beats/sec are heard. Thefrequency of the tuning fork is -a)248Hzb)256Hzc)264Hzd)NoneCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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