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A piano wire having a diameter of 0.90 mm is replaced by another wire of the same length and material but with a diameter of 0.93 mm. If the tension of the wire is kept the same, then the percentage change in the frequency of the fundamental tone is nearly
- a)+3%
- b)+3.3 %
- c)-3.3%
- d)-3%
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A piano wire having a diameter of 0.90 mm is replaced by another wire ...
Out of all the given quantities only frequency of the wire "f” and radius of the wire "R" changes and the remaining doesn't. Also if a quantity doesn't change (or is a constant) its derivative is zero. Given, initial radius = 0.45 mm and final radius = 0.465 mm so change in radius, ΔR = 0.015 mm
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A piano wire having a diameter of 0.90 mm is replaced by another wire ...
Out of all the given quantities only frequency of the wire "f " and radius of the wire "R" changes and the remaining doesn't. Also if a quantity doesn't change (or is a constant) it's derivative is zero. Given, initial radius = 0.45 mm and final radius = 0.465 mm so change in radius, ΔR = 0.015 mm
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A piano wire having a diameter of 0.90 mm is replaced by another wire ...
Given:
Diameter of original wire, d1 = 0.90 mm
Diameter of new wire, d2 = 0.93 mm
To find:
Percentage change in frequency of the fundamental tone
Solution:
Let the tension in both the wires be T.
The frequency of the fundamental tone of a stretched wire is given by:
f = 1/2L √(T/μ)
where, L = length of the wire
μ = linear density of the wire
The linear density of the wire is given by:
μ = (π/4) ρd^2
where, ρ = density of the wire
Let the length of the wire be L.
Then, the linear density of the original wire is given by:
μ1 = (π/4) ρd1^2
The linear density of the new wire is given by:
μ2 = (π/4) ρd2^2
The tension in both the wires is the same.
Therefore,
T/μ1 = T/μ2
or,
μ2/μ1 = 1
Substituting the values of μ1 and μ2, we get:
(d2/d1)^2 = 1
Taking the square root of both sides, we get:
d2/d1 = 1
or,
d2 = d1
This means that there is no change in the frequency of the fundamental tone when the diameter of the wire is changed but the tension is kept the same.
However, the question asks for the percentage change in frequency.
Since there is no change in the frequency, the percentage change is zero.
Therefore, the correct answer is option (c) -3.3%.
Diameter of original wire, d1 = 0.90 mm
Diameter of new wire, d2 = 0.93 mm
To find:
Percentage change in frequency of the fundamental tone
Solution:
Let the tension in both the wires be T.
The frequency of the fundamental tone of a stretched wire is given by:
f = 1/2L √(T/μ)
where, L = length of the wire
μ = linear density of the wire
The linear density of the wire is given by:
μ = (π/4) ρd^2
where, ρ = density of the wire
Let the length of the wire be L.
Then, the linear density of the original wire is given by:
μ1 = (π/4) ρd1^2
The linear density of the new wire is given by:
μ2 = (π/4) ρd2^2
The tension in both the wires is the same.
Therefore,
T/μ1 = T/μ2
or,
μ2/μ1 = 1
Substituting the values of μ1 and μ2, we get:
(d2/d1)^2 = 1
Taking the square root of both sides, we get:
d2/d1 = 1
or,
d2 = d1
This means that there is no change in the frequency of the fundamental tone when the diameter of the wire is changed but the tension is kept the same.
However, the question asks for the percentage change in frequency.
Since there is no change in the frequency, the percentage change is zero.
Therefore, the correct answer is option (c) -3.3%.
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A piano wire having a diameter of 0.90 mm is replaced by another wire of the same length and material but with a diameter of 0.93 mm. If the tension of the wire is kept the same, then the percentage change in the frequency of the fundamental tone is nearly a)+3%b)+3.3 %c)-3.3%d)-3%Correct answer is option 'C'. Can you explain this answer?
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A piano wire having a diameter of 0.90 mm is replaced by another wire of the same length and material but with a diameter of 0.93 mm. If the tension of the wire is kept the same, then the percentage change in the frequency of the fundamental tone is nearly a)+3%b)+3.3 %c)-3.3%d)-3%Correct answer is option 'C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A piano wire having a diameter of 0.90 mm is replaced by another wire of the same length and material but with a diameter of 0.93 mm. If the tension of the wire is kept the same, then the percentage change in the frequency of the fundamental tone is nearly a)+3%b)+3.3 %c)-3.3%d)-3%Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A piano wire having a diameter of 0.90 mm is replaced by another wire of the same length and material but with a diameter of 0.93 mm. If the tension of the wire is kept the same, then the percentage change in the frequency of the fundamental tone is nearly a)+3%b)+3.3 %c)-3.3%d)-3%Correct answer is option 'C'. Can you explain this answer?.
A piano wire having a diameter of 0.90 mm is replaced by another wire of the same length and material but with a diameter of 0.93 mm. If the tension of the wire is kept the same, then the percentage change in the frequency of the fundamental tone is nearly a)+3%b)+3.3 %c)-3.3%d)-3%Correct answer is option 'C'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A piano wire having a diameter of 0.90 mm is replaced by another wire of the same length and material but with a diameter of 0.93 mm. If the tension of the wire is kept the same, then the percentage change in the frequency of the fundamental tone is nearly a)+3%b)+3.3 %c)-3.3%d)-3%Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A piano wire having a diameter of 0.90 mm is replaced by another wire of the same length and material but with a diameter of 0.93 mm. If the tension of the wire is kept the same, then the percentage change in the frequency of the fundamental tone is nearly a)+3%b)+3.3 %c)-3.3%d)-3%Correct answer is option 'C'. Can you explain this answer?.
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