A sound wave is given the following equation:

y = 8 sin (512πt) where t = time in seconds.

How many cycles will occur between t=2 and t=3.5 seconds?

384

Step-by-step explanation:

Standard equation of a sine wave is:

y = A sin (2πf x + B) + C

where A is the amplitude, f is the frequency, B is the phase shift, and C is the vertical offset.

In this case:

2πf = 512π

f = 256

This means there are 256 cycles per second. The number of cycles between t = 2 and t = 3.5 is:

(3.5 - 2) * 256

384