Solve the Problem $y = \sin ( 2 \pi l t )$

question 67

Multiple Choice

Solve the problem.
-On a Touch-Tone phone, each button produces a unique sound. The sound produced is the sum of two tones, gi $y = \sin ( 2 \pi l t )$ and $y = \sin ( 2 \pi h t )$
where $l$ and h are the low and high frequencies (cycles per second) shown on the illustration.


The sound produced is thus given by
$$y = \sin ( 2 \pi l t ) + \sin ( 2 \pi h t )$$
Write the sound emitted by touching the 4 key as a product of sines and cosines.

• A) \(y = 2 \sin ( 439 \pi t ) \cos ( 1,979 \pi t )\)
• B) \(y = 2 \sin ( 566 \pi t ) \cos ( 2,106 \pi t )\)
• C) \(y = 2 \sin ( 2,106 \pi t ) \cos ( 566 \pi t )\)
• D) \(y = 2 \sin ( 1,979 \pi t ) \cos ( 439 \pi t )\)

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