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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 14位,34位,54位

Thus the outcome is L=m位4

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

In order to make the connection with frequency, the wave has speed v and wavelength 位and the frequency could be found as v=位f鈬�f=v位

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

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Most popular questions from this chapter

Two microwave signals of nearly equal wavelengths can generate a beat frequency if both are directed onto the same microwave detector. In an experiment, the beat frequency is 100 MHz. One microwave generator is set to emit microwaves with a wavelength of 1.250 cm. If the second generator emits a longer wavelength, what is that wavelength?

M?

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

A 44-cm-diameter water tank is filled with 35 cm of water. A 3.0-mm-diameter spigot at the very bottom of the tank is opened and water begins to flow out. The water falls into a 2.0-cm-diameter, 40-cm-tall glass cylinder. As the water falls and creates noise, resonance causes the column of air in the cylinder to produce a tone at the column鈥檚 fundamental frequency. What are (a) the frequency and (b) the rate at which the frequency is changing (Hz/s) when the cylinder has been filling for 4.0 s? You can assume that the height of the water in the tank does not appreciably change in 4.0 s.

|| The three identical loudspeakers

in FIGURE P17.71 play a 170 Hz tone

in a room where the speed of sound

is 340 m/s. You are standing 4.0 m

in front of the middle speaker. At

this point, the amplitude of the wave

from each speaker is a.

a. What is the amplitude at this

point?

b. How far must speaker 2 be moved

to the left to produce a maximum

amplitude at the point where you

are standing?

c. When the amplitude is maximum,

by what factor is the sound intensity

greater than the sound intensity from a single speaker?
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