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## Q. 5.3.10

Frequency of a sine wave

Find the frequency of the sine wave given by y = sin(524πx).

## Verified Solution

First find the period:

$P=\frac{2 \pi}{524 \pi}=\frac{1}{262} \approx 0.004$

Since F = 1/P, the frequency is 262. A sine wave with this frequency completes 262 cycles for x in [0, 1] or approximately one cycle in [0, 0.004].

We cannot draw a graph showing 262 cycles in an interval of length one, but we can see the cycle that occurs in the interval [0, 0.004] by looking at Fig. 5.57.