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Touch-Tone Telephones When a key is pressed on a touchtone telephone, the keypad generates two pure tones, which combine to produce a sound that uniquely identifies the key. The figure shows the low frequency f1 and the high frequency f2 associated with each key. Pressing a key produces the sound wave y = sin(2πf1t) + sin(2πf2t).
- (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 t = 0 to t = 0.006 s.
(a)
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To find: The function that models the sound produced when 4 key is pressed.
Answer to Problem 108E
The function that models the sound produced when 4 key is pressed is
Explanation of Solution
Given:
Pressed key produces the sound wave
Calculation:
When the 4 key is pressed, it produces a low frequency sound
The sound wave produced is
Substitute the value of
Hence, the function that models the sound produced when 4 key is pressed is
(b)
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To express: The sound generated by the 4 key as a product of a sine and a cosine function.
Answer to Problem 108E
The sound generated by the 4 key as a product of a sine and a cosine function is
Explanation of Solution
Formula used:
Sum-To-Product formulae:
Calculation:
Since
Simplify further.
Hence, the sound generated by the 4 key as a product of a sine and a cosine function
(c)
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To sketch: The sound wave generated by the key 4 from
Answer to Problem 108E
Use online graphing calculator to sketch the graph of the functions
Explanation of Solution
Calculation:
Use online graphing calculator to sketch the graph of the functions
From Figure 1, it is observed that the sound wave generated by the key 4 from
Chapter 7 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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