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Grade 12Engineering Entrance Exams

A wire under tension vibrates with a frequency of 450 cycles per sound. What would be the fundamental frequency if the wire were half as long, twice as thick and under one fourth tension (a) 225 cps (b) 190 cps (c) 247 cps (d) 174 cps

Profile image of Shwetabh
12 Years agoGrade 12
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2 Answers

Profile image of Saurabh Koranglekar
6 Years ago
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Profile image of Vikas TU
6 Years ago
As per the question,
Given data:
A wire under tension vibrates with a frequency = 450 hertz
According to the speed of the string, we have
v = sqrt[(T-l)/m]
Let V₁ = 450 Hz
Now,
The wire were half as long twice as thick and under one-fourth tention:
New length = l/4
m = 2m
V1 = sqrt[(T-l)/m]

And
V2 = sqrt[(T-l)/2m-4]

Divide V₂ by V₁, we get

∴ v₂ = 159.12 Hz
Hence, the fundamental frequency = 159.12 Hz

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