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Chapter 17: Q. 62 (page 486)

Two loudspeakers emit sound waves along the x-axis. A listener in front of both speakers hears a maximum sound intensity when speaker 2 is at the origin and speaker 1 is at x = 0.50 m. If speaker 1 is slowly moved forward, the sound intensity decreases and then increases, reaching another maximum when speaker 1 is at x = 0.90 m.

a. What is the frequency of the sound? Assume vsound = 340 m/s.

b. What is the phase difference between the speakers?

Short Answer

Expert verified

a) The frequency of the sound is 850 Hz

b) The difference between the speakers areπ/2

Step by step solution

01

Understanding the frequency of the sound 

The frequency of the sound is the number of occurrences of repertaing events per unit.

02

Understanding the frequency of the sound 

The two consecutive maxima are given with two consecutive positions in which the phase difference is 0. On the other hand, based on the provided information it is∆∅=2π∆xλ

Thus, the distance between the consecutive maxima is similar to the wavelength, thus, the wavelength is, λ=0.9-0.5=0.4m

Thus, the frequency is f=vλ=3400.4=850Hz

Since the maxima are at x=0.5 then the phase difference will be 0. The phase difference is coming from the position of the signal phase difference. In numerically,

∆∅=2π∆xλ+∆∅0=0

Thus the difference is∆∅=-2π0.50.4=-5π2=-π2

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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?

qasdff

||| A water wave is called a deep-water wave if the water’s depth

is more than one-quarter of the wavelength. Unlike the waves

we’ve considered in this chapter, the speed of a deep-water wave

depends on its wavelength:

v = B

gl

2p

Longer wavelengths travel faster. Let’s apply this to standing waves.

Consider a diving pool that is 5.0 m deep and 10.0 m wide. Standing

water waves can set up across the width of the pool. Because

water sloshes up and down at the sides of the pool, the boundary

conditions require antinodes at x = 0 and x = L. Thus a standing

water wave resembles a standing sound wave in an open-open tube.

a. What are the wavelengths of the first three standing-wave

modes for water in the pool? Do they satisfy the condition for

being deep-water waves?

b. What are the wave speeds for each of these waves?

c. Derive a general expression for the frequencies fm of the possible

standing waves. Your expression should be in terms of m, g, and L.

d. What are the oscillation periods of the first three standing wave

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?

The two highest-pitch strings on a violin are tuned to 440 Hz (the A string) and 659 Hz (the E string). What is the ratio of the mass of the A string to that of the E string? Violin strings are all the same length and under essentially the same tension.

See all solutions

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