the middle-c hammer of a piano hits two strings, producing beats of 1.25 hz. one of the strings is turned to 240.00 hz. what frequencies (in hz) could the other string have? (answer to the nearest 0.1 hz.)

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15-12-2022
Physics

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the middle-c hammer of a piano hits two strings, producing beats of 1.25 hz. one of the strings is turned to 240.00 hz. what frequencies (in hz) could the other string have? (answer to the nearest 0.1 hz.)

Answer :

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tutorconsortium631 tutorconsortium631 · Answer 1 · 2022-12-21T02:16:53-05:00

The beating phenomenon is the periodic change in intensity at a specific location caused by the superposition of two waves with marginally differing frequencies. (f2 = 241.2 or 238.7 Hz.)

How to solve ?

The frequency of the beat is found from Equation (*):

f beat =∣f 1 −f 2∣=1.25Hz

∣240Hz−f 2∣=1.25Hz

where f2 is the frequency of the other string. In order to solve this equation, we make it into two separate equation and solve them separately:

240Hz−f 2 =1.25Hz

f 2 =240Hz−1.25Hz=238.7Hz

or, 240Hz−f 2 =−1.25Hz

f 2 =240 Hz+1.25Hz=241.2Hz

Therefore, the two possible frequencies of the other string are: f2= 238.7 Hz or 241.2 Hz.

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