Question

a wave has a wavelength of 8.96 x 10^{-1} m and a frequency of 7.62 x 10^{6} hz. determine the speed of the wave. answer: check

Explanation:

Step1: Recall the wave - speed formula

The formula for the speed of a wave is \(v = \lambda\times f\), where \(v\) is the speed, \(\lambda\) is the wavelength, and \(f\) is the frequency.

Step2: Substitute the given values

Given \(\lambda=8.96\times 10^{-1}\text{ m}\) and \(f = 7.62\times 10^{6}\text{ Hz}\).

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Step3: Calculate the numerical and exponential parts separately

First, calculate \(8.96\times7.62 = 68.2752\).
Second, use the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\), so \(10^{-1}\times10^{6}=10^{-1 + 6}=10^{5}\).
Then \(v = 68.2752\times10^{5}\text{ m/s}\).

Step4: Express in scientific notation

\(v=6.82752\times 10^{6}\text{ m/s}\approx6.83\times 10^{6}\text{ m/s}\)

Answer:

\(6.83\times 10^{6}\text{ m/s}\)