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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

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

Grade:Upto college level

2 Answers

Arun
25750 Points
3 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
Vikas TU
14149 Points
3 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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