On a Touch-Tone phone, each button produces a unique sound. The sound produced is the sum of two tones, given by y = sin(2lt) and

On a Touch-Tone phone, each button produces a unique sound. The sound produced is the sum of two tones, given by

y = sin(2πlt)          and              y = sin(2πht)

Where l and hare the low and high frequencies (cycles per second) shown on the illustration. For example, if you touch 7, the low frequency is cycles per second and the high frequency is cycles per second. The sound emitted by touching 7 is 

y = sin[2π(852)t] + sin[2π(1209)t]

(a) Write this sound as a product of sines and/or cosines.

(b) Determine the maximum value of y.

(c) Graph the sound emitted by touching 7.

Touch-Tone phone 697 1- 2)- 3 cycles/sec 770 5 - 6 cycles/sec 852 7- 8 - 9 cycles/sec 941 cycles/sec 1209 cycles/sec 1477 cycles/sec 1336 cycles/sec