Question

The carrier wave for a certain FM radio station can be modelled by the equation $y=A\sin \left({10}^7·2\pi t\right)$, where (A) represents the amplitude of wave and (t) represents the time in seconds. Determine the period of the carrier wave.

Short answer

The period of the carrier wave is $\frac{1}{{10}^7}$seconds.

Step-by-step solution

Step 1. Write down the given information.

The carrier wave for a certain FM radio station can be modelled by the equation $y=A\sin \left({10}^7·2\pi t\right)$, where (A) represents the amplitude of wave and (t) represents the time in seconds.

Step 2. Calculation.

From the given equation$y=A\sin \left({10}^7·2\pi t\right)$, the period $\left(P\right)$of the carrier wave is evaluated as:

$\begin{array}{c}P=\frac{2\pi }{{10}^7\cdot 2\pi }\\ =\frac{1}{{10}^7}\end{array}$

Hence, the period of the carrier wave is $\frac{1}{{10}^7}$ seconds.

Step 3. Conclusion.

The period of the carrier wave is $\frac{1}{{10}^7}$ seconds.