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In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true?
- a)The speed of sound determined from this experiment is 332 ms-1
- b)The end correction in this experiment is 0.9 cm
- c)The wavelength of the sound wave is 66.4 cm
- d)The resonance at 50.7 cm corresponds to the fundamental harmonic
Correct answer is option 'A,C'. Can you explain this answer?
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Speed of sound calculation:
- The speed of sound can be calculated using the formula v = fλ, where v is the speed of sound, f is the frequency of the tuning fork (500 Hz), and λ is the wavelength of the sound wave.
- Since the two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm, the wavelength of the sound wave can be calculated as λ = 2(L2 - L1), where L1 = 50.7 cm and L2 = 83.9 cm.
- Therefore, λ = 2(83.9 cm - 50.7 cm) = 66.4 cm.
- Substituting the values of f = 500 Hz and λ = 66.4 cm into the formula v = fλ, we get v = 500 Hz x 66.4 cm = 33200 cm/s = 332 m/s.
End correction calculation:
- The end correction can be calculated as the difference between the observed length of the air column and the actual length of the air column.
- In this experiment, the observed lengths of the air columns are 50.7 cm and 83.9 cm. The actual length of the air column can be calculated by subtracting the end correction from the observed length.
- Therefore, the end correction = 83.9 cm - 50.7 cm = 33.2 cm.
- Since the actual length of the air column is the sum of the observed length and the end correction, the actual length = observed length + end correction = 50.7 cm + 33.2 cm = 83.9 cm.
- This confirms that the end correction in this experiment is 0.9 cm.
Therefore, the correct statements are:
- The speed of sound determined from this experiment is 332 ms-1 (Option A)
- The wavelength of the sound wave is 66.4 cm (Option C).
- The speed of sound can be calculated using the formula v = fλ, where v is the speed of sound, f is the frequency of the tuning fork (500 Hz), and λ is the wavelength of the sound wave.
- Since the two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm, the wavelength of the sound wave can be calculated as λ = 2(L2 - L1), where L1 = 50.7 cm and L2 = 83.9 cm.
- Therefore, λ = 2(83.9 cm - 50.7 cm) = 66.4 cm.
- Substituting the values of f = 500 Hz and λ = 66.4 cm into the formula v = fλ, we get v = 500 Hz x 66.4 cm = 33200 cm/s = 332 m/s.
End correction calculation:
- The end correction can be calculated as the difference between the observed length of the air column and the actual length of the air column.
- In this experiment, the observed lengths of the air columns are 50.7 cm and 83.9 cm. The actual length of the air column can be calculated by subtracting the end correction from the observed length.
- Therefore, the end correction = 83.9 cm - 50.7 cm = 33.2 cm.
- Since the actual length of the air column is the sum of the observed length and the end correction, the actual length = observed length + end correction = 50.7 cm + 33.2 cm = 83.9 cm.
- This confirms that the end correction in this experiment is 0.9 cm.
Therefore, the correct statements are:
- The speed of sound determined from this experiment is 332 ms-1 (Option A)
- The wavelength of the sound wave is 66.4 cm (Option C).
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In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true?a)The speed of sound determined from this experiment is 332 ms-1b)The end correction in this experiment is 0.9 cmc)The wavelength of the sound wave is 66.4 cmd)The resonance at 50.7 cm corresponds to the fundamental harmonicCorrect answer is option 'A,C'. Can you explain this answer?
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In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true?a)The speed of sound determined from this experiment is 332 ms-1b)The end correction in this experiment is 0.9 cmc)The wavelength of the sound wave is 66.4 cmd)The resonance at 50.7 cm corresponds to the fundamental harmonicCorrect 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 In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true?a)The speed of sound determined from this experiment is 332 ms-1b)The end correction in this experiment is 0.9 cmc)The wavelength of the sound wave is 66.4 cmd)The resonance at 50.7 cm corresponds to the fundamental harmonicCorrect 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 In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true?a)The speed of sound determined from this experiment is 332 ms-1b)The end correction in this experiment is 0.9 cmc)The wavelength of the sound wave is 66.4 cmd)The resonance at 50.7 cm corresponds to the fundamental harmonicCorrect answer is option 'A,C'. Can you explain this answer?.
In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true?a)The speed of sound determined from this experiment is 332 ms-1b)The end correction in this experiment is 0.9 cmc)The wavelength of the sound wave is 66.4 cmd)The resonance at 50.7 cm corresponds to the fundamental harmonicCorrect 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 In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true?a)The speed of sound determined from this experiment is 332 ms-1b)The end correction in this experiment is 0.9 cmc)The wavelength of the sound wave is 66.4 cmd)The resonance at 50.7 cm corresponds to the fundamental harmonicCorrect 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 In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true?a)The speed of sound determined from this experiment is 332 ms-1b)The end correction in this experiment is 0.9 cmc)The wavelength of the sound wave is 66.4 cmd)The resonance at 50.7 cm corresponds to the fundamental harmonicCorrect answer is option 'A,C'. Can you explain this answer?.
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