A wave moves with speed $300 {m s}^{- 1}$ on a wire which is under a tension of $500 N$ . Find how much the tension must be changed to increase the speed to $360 {m s}^{- 1}$ .

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Solution

$V = \sqrt{\frac{T}{M}}$ $T =$ Tension
$M =$ mass per unit length
when $T = 500 N$ and $V = 300 \frac{m}{s}$
$300 = \sqrt{\frac{500}{M}} \Rightarrow M = \frac{1}{180}$
$= 5.556 \times 10^{- 3} k g m$
when,
$v = 360 m s^{- 1}$ and $M = \frac{1}{180}$
Then $T = V^{2} M = 720 N$
$T = Δ = 720 - 500 = 220 N$
$Δ = 360 - 300 = 60 m s^{- 1}$

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A wave moves with speed 300 ms−1 on a wire which is under a tension of 500 N. Find how much the tension must be changed to increase the speed to 360 ms−1.

V=√TM T= Tension M= mass per unit lengthwhen T=500 N and V=300ms300=√500M⇒M=1180=5.556×10−3 kgmwhen,v=360 ms−1 and M=1180Then T=V2M=720 NT=Δ=720−500=220 NΔ=360−300=60 ms−1

A wave moves with speed $300 {m s}^{- 1}$ on a wire which is under a tension of $500 N$ . Find how much the tension must be changed to increase the speed to $360 {m s}^{- 1}$ .