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Chapter 17: Q. 57 (page 486)

A 25-cm-long wire with a linear density of 20 g/m passes across the open end of an 85-cm-long open-closed tube of air. If the wire, which is fixed at both ends, vibrates at its fundamental frequency, the sound wave it generates excites the second vibrational mode of the tube of air. What is the tension in the wire? Assume vsound = 340 m/s.

Short Answer

Expert verified

The tension in the wire is 450N

Step by step solution

01

The concept of the tension in the wire

The force that is transmitted in a cable, rope, wire, or in string the forces acts as a tethering element and works on the opposite ends of the elements.

02

The explanation of the numerical differences in the tension that develops in the wire 

the frequency could be expressed by generating the string by receiving the open-close tube that contains air. Here, the wire will be denoted as w and the tube is t. Thus, the value ismwvw2Lw=f=mtvt4Lt

Therefore, the speed is

vw=Tμ

The expression of the tension is T=v2wμ

From the first equation, the speed of the sound that existed in the wire is vw=(mtvtLw2Ltmw)2μ

The known numerical value will be T=(mtvtLw2Ltmw)2μ

The known numerical value will be

T=(3·340·0.252·0.85·1)2·0.02=450N

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