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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 130 MHz . One microwave generator is set to emit microwaves with a wavelength of 1.250cm. If the second generator emits the longer wavelength, what is that wavelength? Express your answer to four significant figures and include the appropriate units.

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hamzaahmeds

Answer:

The wavelength of second generator is found to be 1.257 cm.

Explanation:

Let,

fb = beat frequency

f1 = frequency of given wave

f2 = frequency of second generator

λ1 = wavelength of given generator = 1.250 cm = 0.0125 m

λ2 = wavelength of second generator

since,

fb = |f1 - f2|

therefore,

fb = c/λ1 - c/λ2

1/λ2 = 1/λ1 - fb/c  

1/λ2 = 1/0.0125 m - (130,000,000 Hz)/(300,000,000 m/s) + 1/0.0125 m

λ2 = 1/79.566

λ2 = 0.01257 m = 1.257 cm

adefioyelaoye

The wavelength of second generator will be 1.257 cm.

What is Wavelength?

This is defined as the distance between corresponding points of two consecutive waves.

Parameters

fb = beat frequency = 130MHz

f1 = frequency of first wave

f2 = frequency of second generator

λ1 = wavelength of first generator = 1.250 cm = 0.0125 m

λ2 = wavelength of second generator

fb = |f1 - f2|

fb = c/λ1 - c/λ2

1/λ2 = 1/λ1 - fb/c  

1/λ2 = 1/0.0125 m - (130,000,000 Hz)/(300,000,000 m/s) + 1/0.0125 m

λ2 = 1/79.566

λ2 = 0.01257 m = 1.257 cm

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