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Grade Upto college level Engineering 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 sumit kumar
12 Years agoGrade Upto college level
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2 Answers

Profile image of Arun
6 Years ago
A wire under tension vibrates with a frequency = 450 hertz
According to the speed of the string, we have
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
And
Divide V₂ by V₁, we get
∴ v₂ = 159.12 Hz
Hence, the fundamental frequency = 159.12 Hz
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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