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A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416Hz. If the length is doubled keeping other things same,the string will
- a)vibrate with a frequency of 416 Hz
- b)vibrate with a frequency of 208 Hz
- c)vibrate with a frequency of 832 Hz
- d)stop vibrating
Correct answer is option 'A'. Can you explain this answer?
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A sonometer wire of length l vibrates in fundamental mode when excited...
Sonometer Wire Vibration and Frequency
Sonometer wire is a musical instrument used to produce sound waves of different frequencies. The wire is stretched between two fixed points and can be made to vibrate by plucking, striking, or rubbing it.
Fundamental mode refers to the lowest frequency at which the wire can vibrate. In this mode, the wire vibrates as a single segment, with nodes at both ends and an antinode in the middle. The frequency of vibration is given by the formula:
f = (1/2l) √(T/μ)
where f is the frequency of vibration, l is the length of the wire, T is the tension in the wire, and μ is the linear density of the wire.
Given that the sonometer wire vibrates in fundamental mode at a frequency of 416 Hz, we can use the above formula to find the length of the wire:
l = (1/2) (T/μ) (1/f^2)
l = (1/2) (T/μ) (1/416^2)
l = 0.0000305 T/μ
Doubling the Length of Wire
If the length of the wire is doubled, its frequency of vibration will change. To find the new frequency, we can use the same formula as before, but with the new length:
f' = (1/2l') √(T/μ)
f' = (1/4l) √(T/μ)
f' = (1/2) f
Therefore, the wire will vibrate with a frequency of 416 Hz even when the length is doubled. This is because the frequency of vibration is inversely proportional to the length of the wire in the fundamental mode. Doubling the length reduces the frequency by a factor of 2, but halving it again brings it back to the original value.
Therefore, the correct answer is option 'A': the wire will vibrate with a frequency of 416 Hz when its length is doubled.
Sonometer wire is a musical instrument used to produce sound waves of different frequencies. The wire is stretched between two fixed points and can be made to vibrate by plucking, striking, or rubbing it.
Fundamental mode refers to the lowest frequency at which the wire can vibrate. In this mode, the wire vibrates as a single segment, with nodes at both ends and an antinode in the middle. The frequency of vibration is given by the formula:
f = (1/2l) √(T/μ)
where f is the frequency of vibration, l is the length of the wire, T is the tension in the wire, and μ is the linear density of the wire.
Given that the sonometer wire vibrates in fundamental mode at a frequency of 416 Hz, we can use the above formula to find the length of the wire:
l = (1/2) (T/μ) (1/f^2)
l = (1/2) (T/μ) (1/416^2)
l = 0.0000305 T/μ
Doubling the Length of Wire
If the length of the wire is doubled, its frequency of vibration will change. To find the new frequency, we can use the same formula as before, but with the new length:
f' = (1/2l') √(T/μ)
f' = (1/4l) √(T/μ)
f' = (1/2) f
Therefore, the wire will vibrate with a frequency of 416 Hz even when the length is doubled. This is because the frequency of vibration is inversely proportional to the length of the wire in the fundamental mode. Doubling the length reduces the frequency by a factor of 2, but halving it again brings it back to the original value.
Therefore, the correct answer is option 'A': the wire will vibrate with a frequency of 416 Hz when its length is doubled.
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A sonometer wire of length l vibrates in fundamental mode when excited...
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A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416Hz. If the length is doubled keeping other things same,the string willa)vibrate with a frequency of 416 Hzb)vibrate with a frequency of 208 Hzc)vibrate with a frequency of 832 Hzd)stop vibratingCorrect answer is option 'A'. Can you explain this answer?
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A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416Hz. If the length is doubled keeping other things same,the string willa)vibrate with a frequency of 416 Hzb)vibrate with a frequency of 208 Hzc)vibrate with a frequency of 832 Hzd)stop vibratingCorrect answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416Hz. If the length is doubled keeping other things same,the string willa)vibrate with a frequency of 416 Hzb)vibrate with a frequency of 208 Hzc)vibrate with a frequency of 832 Hzd)stop vibratingCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416Hz. If the length is doubled keeping other things same,the string willa)vibrate with a frequency of 416 Hzb)vibrate with a frequency of 208 Hzc)vibrate with a frequency of 832 Hzd)stop vibratingCorrect answer is option 'A'. Can you explain this answer?.
A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416Hz. If the length is doubled keeping other things same,the string willa)vibrate with a frequency of 416 Hzb)vibrate with a frequency of 208 Hzc)vibrate with a frequency of 832 Hzd)stop vibratingCorrect answer is option 'A'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416Hz. If the length is doubled keeping other things same,the string willa)vibrate with a frequency of 416 Hzb)vibrate with a frequency of 208 Hzc)vibrate with a frequency of 832 Hzd)stop vibratingCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416Hz. If the length is doubled keeping other things same,the string willa)vibrate with a frequency of 416 Hzb)vibrate with a frequency of 208 Hzc)vibrate with a frequency of 832 Hzd)stop vibratingCorrect answer is option 'A'. Can you explain this answer?.
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