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Chapter 17: Q. 11 (page 483)

A heavy piece of hanging sculpture is suspended by a 90-cmlong, 5.0 g steel wire. When the wind blows hard, the wire hums at its fundamental frequency of 80 Hz. What is the mass of the sculpture?

Short Answer

Expert verified

The mass of the sculpture is 12 kg.12kg.

Step by step solution

01

Given information

The length of the wire is L=90cm=0.90m

The mass of the steel wire is m=5.0g=5脳10-3kg

The fundamental frequency isf=80Hz

02

mass of the sculpture 

For the stretched wire vibrating at its fundamental frequency, the wavelength of the standing wave is given by 位=2L.

The wave speed on the steel wire is

vwire=f位=f2L=80脳2脳0.90=144m/s

The linear density is given by

渭=mL=5脳10-30.90=5.555脳10-3kg/m

The wave speed is also given as role="math" localid="1650002637854" v=Ts渭.

The tension Tsin the wire equals the weight of the sculpture or Mg. Thus,

v=Mg渭M=v2渭g=1442脳5.555脳10-39.8=12kg

Therefore, the mass of the sculpture is 12kg.

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