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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

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?

Deep-sea divers often breathe a mixture of helium and oxygen to avoid getting the “bends” from breathing high-pressure nitrogen. The helium has the side effect of making the divers’ voices sound odd. Although your vocal tract can be roughly described as an open-closed tube, the way you hold your mouth and position your lips greatly affects the standing-wave frequencies of the vocal tract. This is what allows different vowels to sound different. The “ee” sound is made by shaping your vocal tract to have standing- wave frequencies at, normally, 270 Hz and 2300 Hz. What will these frequencies be for a helium-oxygen mixture in which the speed of sound at body temperature is 750 m/s? The speed of sound in air at body temperature is 350 m/s.

A very thin oil film n=1.25floats on watern=1.33.

What is the thinnest film that produces a strong reflection for

green light with a wavelength of 500 nm?

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?

We can make a simple model of the human vocal tract as an open-closed tube extending from the opening of the mouth to the diaphragm. What is the length of this tube if its fundamental frequency equals a typical speech frequency of 250 Hz? The speed of sound in the warm air is 350 m/s.
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