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Chapter 17: Q. 70 (page 486)

Two identical loudspeakers separated by distance ∆xeach

emit sound waves of wavelength λ and amplitude a along the

x-axis. What is the minimum value of the ratio ∆xλ for which

the amplitude of their superposition is also a?

Short Answer

Expert verified

The solution also provides the identical distance of the sound waves of the wavelengths

Step by step solution

01

Discussion on superposition

When two or more waves cross at a point, the displacement at that point is equal to the sum of the displacements of the individual waves.

02

Discusion on the phase difernces

The phrase difference is calculated below

@acos(π∆xλ)=a=cos(π∆xλ)=1/2=A=2aco9s(∆∅2)∆∅=2π∆xλA=2acos(π∆xλ)=π/3∆xλ=1/3

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Most popular questions from this chapter

FIGURE EX17.7 shows a standing wave on a string that is oscillating at 100 Hz. a. How many antinodes will there be if the frequency is increased to 200 Hz? b. If the tension is increased by a factor of 4, at what frequency will the string continue to oscillate as a standing wave that looks like the one in the figure?

A longitudinal standing wave can be created in a long, thin aluminum rod by stroking the rod with very dry fingers. This is often done as a physics demonstration, creating a high-pitched, very annoying whine. From a wave perspective, the standing wave is equivalent to a sound standing wave in an open-open tube. As FIGURE EX17.21 shows, both ends of the rod are antinodes. What is the fundamental frequency of a 2.0-m-long aluminum rod?

A steel wire is used to stretch the spring of FIGURE P17.42. An oscillating magnetic field drives the steel wire back and forth. A standing wave with three antinodes is created when the spring is stretched 8.0 cm. What stretch of the spring produces a standing wave with two antinodes?

Two loudspeakers in a plane, 5.0 m apart, are playing the same frequency. If you stand 12.0 m in front of the plane of the speakers, centered between them, you hear a sound of maximum intensity. As you walk parallel to the plane of the speakers, staying 12.0 m in front of them, you first hear a minimum of sound intensity when you are directly in front of one of the speakers. What is the frequency of the sound? Assume a sound speed of 340 m/s.

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