Problem Solving Equation

Question

A sound wave has an equation.

y= 7 sin(58πt) where t= time in seconds.

What is the frequency?

Answer 1

d/t=v

As for sound it depends where it's traveling: water,air,space etc.

What does "y" represent? Either distance or velocity.

Answer 2

Great question! When the equation for a wave is written in the format

A sin(B(t + C)) + D, every coefficient means something.

A (7 in the example) is the AMPLITUDE of the wave - how big does it get?

B (58 * π) in the example is the ANGULAR FREQUENCY (also written as ω) - how quickly does the wave go through one period?

C (0 in the example) is the PHASE SHIFT - where does the wave start?

D (0 in the example) is the CENTER VALUE - around what value does the wave oscillate (go from its highest value to its smallest value). This is the value in the middle.

The part of the equation we care about here is 58*π. You can find the frequency from the angular frequency:

2πf = ω

2πf = 58π

f = 58π/2π

f = 29 1/seconds = 29 Hz.