Two nearby trumpets are sounded together and a beat frequency of 8 Hz is heard. If one of the trumpets sounds at a frequency of 871 Hz, what are the two possible frequencies of the other trumpet? (Enter your answers from the smallest to the largest, in Hz, to three significant figures
Solution:
Beat frequency is defined as the absolute difference between the frequencies produced by the alternating constructive and destructive interference. It is expressed as:
fbeat = f1 - f2
Calculating the first possible frequency produced by the trumpet,
fbeat =| f1 - f2 |
or, 8Hz = 871 - f2
or, f2 = 863 Hz
Calculating the second possible frequency,
fbeat =| f1 - f2 |
Or, 8 Hz = f2 - 871
Or, f2 = 879 Hz
Hence, two possible frequencies are 863 Hz , and 879 Hz
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