Question

Help with this last question

Answer 1

There are actually two beats produced.

Their frequencies are the SUM of the products and the DIFFERENCE of the products.

If you were listening to these two violins playing their individual notes, then there would be four frequencies in the "air" . . . the two originals and the two beats:

988 Hz, 990 Hz, 1,978 Hz, and 2 Hz .

From the list of choices, you should select the first one (2 Hz), even though it doesn't quite tell the whole story.

Answer 2

Hello from MrBillDoesMath

Answer: 2Hz, the first choice

Discussion:

The frequency of the beat is given by the difference of the two frequencies. That is, 990 - 988 Hz = 2Hz, which is the first choice

BTW: Beats are an essential part in the tuning of modern day acoustic pianos. Suppose you wanted to tune the note A that that is one octave above A = 440 Hz. You may think that the higher string is tuned to 440*2 = 880 Hz. Nope. The A = 440 note divides into two parts but because of the stiffness of piano wire the 2nd harmonic (the one you think should be 880) is actually a few hertz higher than 880. To avoid excessive beats (think "interference patterns") the octave higher A must be turned a bit sharper than A = 880. This leads to the term "octave stretching" that all piano tuners must account for,

Thank you,

Mr. B