Physics
Physics
3rd Edition
ISBN: 9780073512150
Author: Alan Giambattista, Betty Richardson, Robert C. Richardson Dr.
Publisher: McGraw-Hill Education
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Chapter 12, Problem 62P
To determine

The weight should she hang from the wire if the temperature is 18.0°C.

Expert Solution & Answer
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Answer to Problem 62P

The weight should she hang from the wire is 1,280N.

Explanation of Solution

Write the expression for the fundamental frequency of the tube.

f1=vair4Ltube (I)

Here, f1 is the fundamental frequency of the wire, vair is the speed of sound in air and Ltube is the length of the tube.

Write the expression for the velocity of air with temperature.

vair=v0TT0

Here, v0 is the speed of sound at 0°Cor273.15K and T is the present temperature and T0 is the 0°Cor273.15K.

Substitute v0TT0 for vair in equation (I) to get f1.

f1=v04LtubeTT0 (II)

Write the expression for appropriate wave speed of the wire.

f1=vwire2Lwire (III)

Here, vwire is the speed of sound in wire and Lwire is the length of wire.

Rearrange above equation to get vwire.

vwire=2Lwiref1

Write the expression for the linear mass density of wire.

μ=mwireLwire (IV)

Here, μ is the linear mass density of the wire, mwire is the mass of the wire and Lwire is the length of the wire.

Write the expression for the mass of the wire.

mwire=ρwireAwireLwire

Here, mwire is the mass of the wire, ρwire is the density of the wire, Awire is the area of cross section of the wire.

Substitute ρwireAwireLwire for mwire in equation (IV) to get μ.

μ=ρwireAwireLwireLwire=ρwireAwire

Write the expression for the weight to be hung from wire.

vwire=Fμ

Substitute ρwireAwire for μ in above equation to get vwire.

vwire=FρwireAwire

Conclusion:

Rearrange above equation to get F.

F=ρwireAwirevwire2

Substitute 2Lwiref1 for vwire in above equation to get vwire.

F=ρwireAwire(2Lwiref1)2

Substitute v04LtubeTT0 for f1 and πr2 for Awire in above equation to get F.

F=ρwireπrwire2(LwireLtube)2v02T4T0 (V)

Convert 18.0°C into Kelvin scale.

18.0°C=(18.0+273.15)K=291.15K

Substitute 7860kg/m3 for ρwire, 0.00200m for rwire, 1.00m for Lwire,1.50m for Ltube, 291.15K for T , 273.15K for T0 and 331.0m/s for v0 in equation (V).

F=(7860kg/m3)π(0.00200m)2(1.00m1.50m)2(331.0m/s)2(291.15K)4(273.15K)=1280N

Therefore, the weight should she hang from the wire is 1,280N.

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Chapter 12 Solutions

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