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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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