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

We are given that \(v = 3.00\times10^{8}\space m/s\) and \(f=9.26\times 10^{7}\space Hz\).
Substitute these values into the formula \(\lambda=\frac{3.00\times 10^{8}}{9.26\times 10^{7}}\).
Using the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\), we have \(\frac{3.00}{9.26}\times10^{8-7}\).
\(\frac{3.00}{9.26}\approx0.324\) and \(10^{8 - 7}=10^{1}\).

Answer:

The wavelength \(\lambda\approx3.24\space m\)