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Low frequencies ABC DEF 697 cycles/sec MNO GHI 770 cycles/sec PRS TUV 852 cycles/sec OPER 941 cycles/sec High frequencies 1209 1477 cycles/sec cycles/sec 1336 cycles/sec

Low frequencies ABC DEF 697 cycles/sec MNO GHI 770 cycles/sec PRS TUV 852 cycles/sec OPER 941 cycles/sec High frequencies 1209 1477 cycles/sec cycles/sec 1336 cycles/sec

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The sound produced by touching each button on a touch-tone phone is
described by y = sin 2* lt + sin 2* ht, where l and h are the low and high frequencies in the figure shown. For example, what sound is produced by touching 5? The low frequency is l = 770 cycles per second and the high
frequency is h = 1336 cycles per second. The sound produced by touching 5 is described by y = sin 2*(770)t + sin 2*(1336)t.

The touch-tone phone sequence for that most naive of melodies is given as follows: Mary Had a Little Lamb 3212333,222,399,3212333322321.

Solve, a. Many numbers do not appear in this sequence, including 7. If you accidently touch 7 for one of the notes, describe this sound as the sum of sines.

b. Describe this accidental sound as a product of sines and cosines.

Low frequencies ABC DEF 697 cycles/sec MNO GHI 770 cycles/sec PRS TUV 852 cycles/sec OPER 941 cycles/sec High frequencies 1209 1477 cycles/sec cycles/sec 1336 cycles/sec
Transcribed Image Text:Low frequencies ABC DEF 697 cycles/sec MNO GHI 770 cycles/sec PRS TUV 852 cycles/sec OPER 941 cycles/sec High frequencies 1209 1477 cycles/sec cycles/sec 1336 cycles/sec
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