116. Touch-Tone Telephones When a key is pressed on a touch- tone telephone, the keypad generates two pure tones, which combine to produce a sound that uniquely identifies the key. The figure shows the low frequency f, and the high fre- quency f2 associated with each key. Pressing a key produces the sound wave y = sin(27ft) + sin(27 fat). (a) Find the function that models the sound produced when the 4 key is pressed. (b) Use a Sum-to-Product Formula to express the sound generated by the 4 key as a product of a sine and a cosine function. (c) Graph the sound wave generated by the 4 key from 1= 0 to 1 = 0.006 s. High frequency f2 1209 1336 1477 Hz. 697 Hz 1 2 Low 770 Hz 4 5 6. frequency fi 852 Hz 7 8 9 941 Hz 23 3.

116. Touch-Tone Telephones When a key is pressed on a touch- tone telephone, the keypad generates two pure tones, which combine to produce a sound that uniquely identifies the key. The figure shows the low frequency f, and the high fre- quency f2 associated with each key. Pressing a key produces the sound wave y = sin(27ft) + sin(27 fat). (a) Find the function that models the sound produced when the 4 key is pressed. (b) Use a Sum-to-Product Formula to express the sound generated by the 4 key as a product of a sine and a cosine function. (c) Graph the sound wave generated by the 4 key from 1= 0 to 1 = 0.006 s. High frequency f2 1209 1336 1477 Hz. 697 Hz 1 2 Low 770 Hz 4 5 6. frequency fi 852 Hz 7 8 9 941 Hz 23 3.