Question

1. a radio station broadcasts its radio signals at a frequency of 9.26 x 10^7 hz. find the wavelength if the waves travel at a speed of 3.00 x 10^8 m/s.

Explanation:

Step1: Recall the wave - speed formula

The formula for the speed of a wave is \(v = f\lambda\), where \(v\) is the speed of the wave, \(f\) is the frequency, and \(\lambda\) is the wavelength. We need to solve for \(\lambda\), so we can rewrite the formula as \(\lambda=\frac{v}{f}\).

Step2: Substitute the given values into the formula

Given \(v = 3.00\times10^{8}\space m/s\) and \(f = 9.26\times10^{7}\space Hz\).

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Step3: Calculate the value

\(\frac{3.00}{9.26}\approx0.324\), and \(10^{8 - 7}=10^{1}\). So \(\lambda = 0.324\times10^{1}=3.24\space m\)

Answer:

The wavelength of the radio waves is \(3.24\space m\)