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Two in-phase loudspeakers, which emit sound in all directions,

are sitting side by side. One of them is moved sideways by 3.0 m, then forward by 4.0 m. Afterward, constructive interference is

observed 14and 34of the distance between the speakers along the line that joins them. What is the maximum possible wavelength of the sound waves?

Short Answer

Expert verified

The maximum possible wavelength of the sound waves is5m.

Step by step solution

01

Given data

Out of two loudspeakers, of them is moved sideways by 3.0 m and then forward by 4.0 m.

A constructive interference is observed 14and 34of the distance between the speakers along the line that joins them.

Therefore, the position of the loudspeakers should be as follows:

02

Determination of the maximum possible wavelength

The final distance between the speakers can be obtained by applying the Pythagorean theorem as,

d=32+42md=25md=5m

Therefore, the position of the loudspeaker should be as given below:

Now, the distance between the two spots producing constructive interference is,

D=345m-145mD=52m

As the constructive interference happens when the distance between the two spots is, D=λ2

Thus, the longest wavelength possible in this situation must beλ2=52mλ=5m

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Most popular questions from this chapter

In 1866, the German scientist Adolph Kundt developed a

technique for accurately measuring the speed of sound in various gases. A long glass tube, known today as a Kundt’s tube, has a vibrating piston at one end and is closed at the other. Very finely ground particles of cork are sprinkled in the bottom of the tube before the piston is inserted. As the vibrating piston is slowly moved forward, there are a few positions that cause the cork particles to collect in small, regularly spaced piles along the bottom. FIGURE P17.53 shows an experiment in which the tube is filled with pure oxygen and the piston is driven at 400 Hz. What is the speed of sound in oxygen?

Analyze the standing sound waves in an open-closed tube to show that the possible wavelengths and frequencies are given by Equation 17.18.

FIGURE Q17.1 shows a standing wave oscillating on a string at frequency f0. a. What mode (m-value) is this? b. How many antinodes will there be if the frequency is doubled to 2f0?

|| 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

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a. What is the amplitude at this

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b. How far must speaker 2 be moved

to the left to produce a maximum

amplitude at the point where you

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c. When the amplitude is maximum,

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What is the fundamental frequency of the steel wire in FIGURE P17.48?

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