Question

1. the speed of light in cold air is approximately 3 x 10^8 meters/sec. the speed of sound in cold air is approximately 3 x 10^2 meters/sec. the speed of light in cold air is how many times the speed of sound in cold air?

Explanation:

Step1: Set up the division formula

To find out how many times the speed of light is compared to the speed of sound, we use the formula \(n=\frac{v_{light}}{v_{sound}}\), where \(v_{light} = 3\times10^{8}\) meters/sec and \(v_{sound}=3\times 10^{2}\) meters/sec. So, \(n=\frac{3\times 10^{8}}{3\times 10^{2}}\).

Step2: Simplify the formula using the rule of exponents \(\frac{a\times10^{m}}{a\times10^{n}}=10^{m - n}\)

First, simplify the coefficients: \(\frac{3}{3}=1\). Then, for the exponents, using the rule \(a^{m}\div a^{n}=a^{m - n}\) (here \(a = 10\)), we have \(10^{8}\div10^{2}=10^{8 - 2}\). So, \(n = 10^{6}\).

Answer:

The speed of light in cold air is \(10^{6}\) times the speed of sound in cold air.