Word Problem Solving Equation

Question

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?

Answer 1

Find the period of the wave, and then divide the time interval by the period. That will give the number of cycles that occur within the time interval.

Time interval Δt:

Δt = (3.5 - 2) s = 1.5 s

Period T:

ω = 512π

T = 2π/ω = 2π/(512π) = 1 / 256 s^-1

number of cycles = Δt / T = ?

Plug in the numbers.