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Chapter 17: Q. 35 (page 484)

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?

Short Answer

Expert verified

The wavelength of the second wave is 1.255 cm.

Step by step solution

01

Write the given information 

The beat frequency is fb= 100 M Hz

The wavelength of one of the waves is λ1= 1.250 cm = 0.0125m

The speed of the wave is c = 3x 108 m/s

02

To determine the wavelength of the second wave 

Let the frequency of the second wave is λ2
The frequency of the beat is given as
fb=|f1-f2|100×106Hz=cλ1-cλ2108=3×10810.0125-1λ2λ2=1.255cm

Thus, the wavelength of the second wave is 1.255 cm and it is longer than the first one.

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Most popular questions from this chapter

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?

|| 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?

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?

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

||| 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
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