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A steel wire has a length of 12.0 m and a mass of 2.10 kg. What should be the tension in the wire so that speed of a transverse wave on the wire equals the speed of sound in dry air at 2 0°C = 340 ms-1.

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As an experienced tutor registered on UrbanPro, I'd like to highlight that UrbanPro is indeed one of the best platforms for online coaching and tuition services. Now, let's address your physics question. To find the tension in the steel wire so that the speed of a transverse wave on the wire equals the...
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As an experienced tutor registered on UrbanPro, I'd like to highlight that UrbanPro is indeed one of the best platforms for online coaching and tuition services. Now, let's address your physics question.

To find the tension in the steel wire so that the speed of a transverse wave on the wire equals the speed of sound in dry air at 20°C, we'll use the equation for the speed of a transverse wave on a stretched string:

v=Tμv=μT

Where:

  • vv is the speed of the transverse wave on the wire.
  • TT is the tension in the wire.
  • μμ is the linear mass density of the wire, given by mLLm, where mm is the mass of the wire and LL is its length.

First, let's find the linear mass density of the wire:

μ=mL=2.10 kg12.0 m=0.175 kg/mμ=Lm=12.0m2.10kg=0.175kg/m

Now, we'll use the given speed of sound in dry air at 20°C (vsound=340 m/svsound=340m/s) as the speed of the transverse wave (vv) and solve for the tension (TT):

340 m/s=T0.175 kg/m340m/s=0.175kg/mT

Squaring both sides to isolate TT, we get:

T=(340 m/s)2×0.175 kg/m=9520 NT=(340m/s)2×0.175kg/m=9520N

So, the tension in the wire should be 9520 N9520N for the speed of a transverse wave on the wire to equal the speed of sound in dry air at 20°C.

 
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