First slide

Standing waves

Question

A wire under tension vibrates with a frequency of 450 per second. What would be the fundamental frequency if the wire were half as long, twice as thick and under one-fourth tension

Easy

A

225cps
B

190 cps
C

247 cps
D

174 cps

Solution

$n = \frac{1}{2 l} \sqrt{(\frac{T}{m})} Here 450 = \frac{1}{2 l} \sqrt{(\frac{T}{m})} o r 450 = \frac{1}{2 l} \sqrt{(\frac{T}{π r^{2} ρ})} n_{2} = \frac{1}{2 (l / 2)} \sqrt{[\frac{(T / 4)}{π (2 r)^{2} ρ}]} Solving, we get n_{2} = 225 H z$

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