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The beat frequency of two frequencies \(f_{1}\) and \(f_{2}\) is a) the absolute value of the sum of the frequencies, \(\left|f_{1}+f_{2}\right|\). b) the absolute value of the difference of the frequencies, \(\left|f_{1}-f_{2}\right|\). c) the average of the two frequencies. d) half of the sum of the two frequencies. e) half of the absolute value of the difference of the two frequencies.

Short Answer

Expert verified
Answer: The beat frequency of two frequencies \(f_{1}\) and \(f_{2}\) is the absolute value of the difference of the frequencies, \(\left|f_{1}-f_{2}\right|\).

Step by step solution

01

Definition of Beat Frequency

The beat frequency (\(f_{beat}\)) of two frequencies (\(f_{1}\) and \(f_{2}\)) is defined as the absolute value of the difference between them. Mathematically, this is represented as: \(f_{beat} = \left|f_{1} - f_{2}\right|\).
02

Comparing the Options

Now, let's compare the given options with the definition of beat frequency: a) \(\left|f_{1}+f_{2}\right|\) - This option represents the sum of the frequencies, not the difference. b) \(\left|f_{1}-f_{2}\right|\) - This option matches the definition of beat frequency. c) The average of the two frequencies - This option does not represent the difference between the frequencies. d) Half of the sum of the two frequencies - This option also does not represent the difference between the frequencies. e) Half of the absolute value of the difference of the two frequencies - This option does not represent the exact difference between the frequencies.
03

Conclusion

Based on the analysis above, the correct answer is option (b): the beat frequency of two frequencies \(f_{1}\) and \(f_{2}\) is the absolute value of the difference of the frequencies, \(\left|f_{1}-f_{2}\right|\).

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Most popular questions from this chapter

Find the resonance frequency of the ear canal. Treat it as a half-open pipe of diameter \(8.0 \mathrm{~mm}\) and length \(25 \mathrm{~mm}\). Assume that the temperature inside the ear canal is body temperature \(\left(37^{\circ} \mathrm{C}\right)\).

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