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Chapter 17: Q. 60 (page 486)

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

Short Answer

Expert verified

The conditions of having one node and one antinode at the end the formulas that one could get are,

Step by step solution

01

The concept of node and antinode 

Node is a point which's amplitude is 0. The point in which amplitude is maximum is known as antinodes.

02

Finding out the frequencies based on the information 

In an open-closed tube, the presence of node and antinode is a must. so, the possible arrangements can reach to 14λ,34λ,54λ

Thus the outcome is L=mλ4

Here m= 1, 3, 5 and the arrangements will be λm=4Lm

In order to make the connection with frequency, the wave has speed v and wavelength λand the frequency could be found as v=λf⇒f=vλ

The substitution of the wavelength isrole="math" localid="1649148923810" fm=mv4L

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Most popular questions from this chapter

||| 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

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?

FIGURE Q17.8 is a snapshot graph of two plane waves passing

through a region of space. Each wave has a 2.0 mm amplitude

and the same wavelength. What is the net displacement of the

medium at points a, b, and c?

A flute filled with helium will, until the helium escapes, play notes at a much higher pitch than normal. Why?

Two radio antennas are separated by 2.0 m. Both broadcast

identical 750 MHz waves. If you walk around the antennas in a

circle of radius 10 m, how many maxima will you detect?
See all solutions

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