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 frequency f, associated with each key. Pressing a key produces the sound wave y= sin(2rtf t) + sin(2a2t). High frequency f2 1209 1336 1477 Hz 697 Hz Low 770 Hz 5 6. frequency 852 Hz 941 Hz . (a) Find the function that models the sound produced when the 9 key is pressed. y = (b) Use a Sum-to-Product Formula to express the sound generated by the 9 key as a product of a sine and a cosine function. y =
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 frequency f, associated with each key. Pressing a key produces the sound wave y= sin(2rtf t) + sin(2a2t). High frequency f2 1209 1336 1477 Hz 697 Hz Low 770 Hz 5 6. frequency 852 Hz 941 Hz . (a) Find the function that models the sound produced when the 9 key is pressed. y = (b) Use a Sum-to-Product Formula to express the sound generated by the 9 key as a product of a sine and a cosine function. y =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![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 \( f_1 \) and the high frequency \( f_2 \) associated with each key. Pressing a key produces the sound wave \( y = \sin(2\pi f_1 t) + \sin(2\pi f_2 t) \).
[Diagram Description: A keypad is shown with frequencies. Arrows link each key to its corresponding frequencies. The low frequencies \( f_1 \) (in Hz) are:
- 697 Hz (keys 1, 2, 3)
- 770 Hz (keys 4, 5, 6)
- 852 Hz (keys 7, 8, 9)
- 941 Hz (keys *, 0, #)
The high frequencies \( f_2 \) (in Hz) are:
- 1209 Hz (keys 1, 4, 7, *)
- 1336 Hz (keys 2, 5, 8, 0)
- 1477 Hz (keys 3, 6, 9, #)]
(a) Find the function that models the sound produced when the 9 key is pressed.
\( y = \) [Answer Box]
(b) Use a Sum-to-Product Formula to express the sound generated by the 9 key as a product of a sine and a cosine function.
\( y = \) [Answer Box]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3ae03bb8-ec3d-406c-93d2-922fad9dd684%2F72e828a7-dac7-4283-ad4d-036582ac71e8%2Fbx7q2kw_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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 \( f_1 \) and the high frequency \( f_2 \) associated with each key. Pressing a key produces the sound wave \( y = \sin(2\pi f_1 t) + \sin(2\pi f_2 t) \).
[Diagram Description: A keypad is shown with frequencies. Arrows link each key to its corresponding frequencies. The low frequencies \( f_1 \) (in Hz) are:
- 697 Hz (keys 1, 2, 3)
- 770 Hz (keys 4, 5, 6)
- 852 Hz (keys 7, 8, 9)
- 941 Hz (keys *, 0, #)
The high frequencies \( f_2 \) (in Hz) are:
- 1209 Hz (keys 1, 4, 7, *)
- 1336 Hz (keys 2, 5, 8, 0)
- 1477 Hz (keys 3, 6, 9, #)]
(a) Find the function that models the sound produced when the 9 key is pressed.
\( y = \) [Answer Box]
(b) Use a Sum-to-Product Formula to express the sound generated by the 9 key as a product of a sine and a cosine function.
\( y = \) [Answer Box]
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