Questions: A sound wave has an equation y=7 sin (58 pi t) where t= time in seconds What is its frequency? [?] cycles/second

Solution Steps

The general form of a sine wave equation is: \[ y = A \sin(2 \pi f t) \] where:

• \(A\) is the amplitude,
• \(f\) is the frequency in cycles per second (Hz),
• \(t\) is the time in seconds.

The given equation is: \[ y = 7 \sin(58 \pi t) \] We need to compare this with the general form \(y = A \sin(2 \pi f t)\).

From the given equation, we see that the argument of the sine function is \(58 \pi t\). In the general form, the argument is \(2 \pi f t\). Therefore, we can set: \[ 58 \pi t = 2 \pi f t \]

To find the frequency \(f\), we divide both sides of the equation by \(2 \pi t\): \[ 58 \pi = 2 \pi f \] \[ f = \frac{58 \pi}{2 \pi} = 29 \]

Final Answer