Question

a wave has a wavelength of 9.23 x 10^{-4} m and a frequency of 4.08 x 10^{3} hz. determine the speed of the wave.

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 \(\lambda=9.23\times 10^{-4}\space m\) and \(f = 4.08\times 10^{3}\space Hz\), substitute into the formula:

$$
LATEXBLOCK0
$$

Step3: Calculate the numerical and exponential parts

First, calculate \(9.23\times4.08 = 37.6584\). Then, calculate \(10^{-4}\times 10^{3}=10^{-1}\) (using the rule \(a^{m}\times a^{n}=a^{m + n}\)).
So, \(v = 37.6584\times10^{-1}\)

Step4: Simplify the result

\(v=3.76584\approx3.77\space m/s\)

Answer:

\(3.77\space m/s\)