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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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Most popular questions from this chapter

What are the three longest wavelengths for standing sound waves in a 121-cm-long tube that is (a) open at both ends and (b) open at one end, closed at the other?

A violinist places her finger so that the vibrating section of a 1.0 g/m string has a length of 30 cm, then she draws her bow across it. A listener nearby in a 20°C room hears a note with a wavelength of 40 cm. What is the tension in the string?

|| The three identical loudspeakers

in FIGURE P17.71 play a 170 Hz tone

in a room where the speed of sound

is 340 m/s. You are standing 4.0 m

in front of the middle speaker. At

this point, the amplitude of the wave

from each speaker is a.

a. What is the amplitude at this

point?

b. How far must speaker 2 be moved

to the left to produce a maximum

amplitude at the point where you

are standing?

c. When the amplitude is maximum,

by what factor is the sound intensity

greater than the sound intensity from a single speaker?

Two loudspeakers emit sound waves along the x-axis. The

sound has maximum intensity when the speakers are 20 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 60 cm.

a. What is the wavelength of the sound?

b. If the distance between the speakers continues to increase, at

what separation will the sound intensity again be a maximum?

Two in-phase speakers 2.0 m apart in a plane are emitting 1800 Hz sound waves into a room where the speed of sound is 340 m/s. Is the point 4.0 m in front of one of the speakers, perpendicular to the plane of the speakers, a point of maximum constructive interference, maximum destructive interference, or something in between?
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