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A string of a musical instrument is 50 cm long and fundamental frequency is 270 Hz. If the desired frequency of 1000Hz is to be produced, the required string length is
- a)13.5 cm
- b)2.7 cm
- c)5.4 cm
- d)10.8 cm
Correct answer is option 'A'. Can you explain this answer?
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A string of a musical instrument is 50 cm long and fundamental frequen...
Calculation of Required String Length to Produce 1000Hz Frequency
Given:
Length of the string = 50 cm
Fundamental frequency = 270 Hz
Desired frequency = 1000 Hz
Formula:
The frequency of a string can be calculated using the following formula:
f = (n/2L) * √(T/μ)
Where,
f = frequency
n = harmonic number
L = length of the string
T = tension in the string
μ = linear density of the string
To produce the desired frequency of 1000 Hz, we can assume the string to be vibrating in its second harmonic (n = 2). Therefore, the formula can be simplified to:
L = (n/2f) * √(T/μ)
Substituting the given values, we get:
L = (2/2*1000) * √(T/μ)
L = 0.001 * √(T/μ)
Now, we need to find the value of T/μ. We can use the fact that the tension and linear density of the string remain constant. Therefore, we can equate the two formulas to get:
(n/2L) * √(T/μ) = (2/2f) * √(T/μ)
n/f = L/f
50/270 = L/1000
L = 13.5 cm
Therefore, the required string length to produce a frequency of 1000 Hz is 13.5 cm. This is the correct answer and matches with option A.
Given:
Length of the string = 50 cm
Fundamental frequency = 270 Hz
Desired frequency = 1000 Hz
Formula:
The frequency of a string can be calculated using the following formula:
f = (n/2L) * √(T/μ)
Where,
f = frequency
n = harmonic number
L = length of the string
T = tension in the string
μ = linear density of the string
To produce the desired frequency of 1000 Hz, we can assume the string to be vibrating in its second harmonic (n = 2). Therefore, the formula can be simplified to:
L = (n/2f) * √(T/μ)
Substituting the given values, we get:
L = (2/2*1000) * √(T/μ)
L = 0.001 * √(T/μ)
Now, we need to find the value of T/μ. We can use the fact that the tension and linear density of the string remain constant. Therefore, we can equate the two formulas to get:
(n/2L) * √(T/μ) = (2/2f) * √(T/μ)
n/f = L/f
50/270 = L/1000
L = 13.5 cm
Therefore, the required string length to produce a frequency of 1000 Hz is 13.5 cm. This is the correct answer and matches with option A.
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A string of a musical instrument is 50 cm long and fundamental frequency is 270 Hz. If the desired frequency of 1000Hz is to be produced, the required string length isa)13.5 cmb)2.7 cmc)5.4 cmd)10.8 cmCorrect answer is option 'A'. Can you explain this answer?
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A string of a musical instrument is 50 cm long and fundamental frequency is 270 Hz. If the desired frequency of 1000Hz is to be produced, the required string length isa)13.5 cmb)2.7 cmc)5.4 cmd)10.8 cmCorrect 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 string of a musical instrument is 50 cm long and fundamental frequency is 270 Hz. If the desired frequency of 1000Hz is to be produced, the required string length isa)13.5 cmb)2.7 cmc)5.4 cmd)10.8 cmCorrect 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 string of a musical instrument is 50 cm long and fundamental frequency is 270 Hz. If the desired frequency of 1000Hz is to be produced, the required string length isa)13.5 cmb)2.7 cmc)5.4 cmd)10.8 cmCorrect answer is option 'A'. Can you explain this answer?.
A string of a musical instrument is 50 cm long and fundamental frequency is 270 Hz. If the desired frequency of 1000Hz is to be produced, the required string length isa)13.5 cmb)2.7 cmc)5.4 cmd)10.8 cmCorrect 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 string of a musical instrument is 50 cm long and fundamental frequency is 270 Hz. If the desired frequency of 1000Hz is to be produced, the required string length isa)13.5 cmb)2.7 cmc)5.4 cmd)10.8 cmCorrect 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 string of a musical instrument is 50 cm long and fundamental frequency is 270 Hz. If the desired frequency of 1000Hz is to be produced, the required string length isa)13.5 cmb)2.7 cmc)5.4 cmd)10.8 cmCorrect answer is option 'A'. Can you explain this answer?.
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