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Chapter 17: Q. 29 (page 484)

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

A sheet of glass is coated with a 500-nm-thick layer of oil 1n = 1.422.

a. For what visible wavelengths of light do the reflected waves interfere constructively?

b. For what visible wavelengths of light do the reflected waves interfere destructively?

c. What is the color of reflected light? What is the color of transmitted light?

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?

A string vibrates at its third-harmonic frequency. The amplitude at a point 30 cm from one end is half the maximum amplitude. How long is the string?

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?

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?

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