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Chapter 8: Q. 53 (page 551)

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)andy=sin(2πht) where l and h are the low and high frequencies (cycles per second) shown in the illustration. For example, if you touch 7, the low frequency is l=852cycles per second and the high frequency is h=1209cycles per second. The sound emitted by touching 7 is y=sin2π(852t)+sin2π(1209t)

Use a graphing utility to graph the sound emitted by touching 7.

Short Answer

Expert verified

The required graph is

Step by step solution

01

Step 1. Given Information

The given figure is

02

Step 2. Explanation

On a touch-tone phone, each button produce a unique sound and the sound produced is the sum of two tones.

For the button key 7, the low frequency is 852 cycles per second and high is 1209 cycles per second.

Thus, the sound emitted by touching 7 is given by,

y=sin2πlt+sin(2πht)y=sin(2π(852)t)+sin(2π(1209)t)y=sin(1704πt)+sin(2418πt)

The graph of the obtained function is

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