Answer:
Wavelength = [tex]4.225\times 10^{-7}\ m[/tex].
Explanation:
Given:
The wave is a light wave. So, speed of light wave is, [tex]c=3\times 10^8\ m/s[/tex]
The frequency of the light wave is, [tex]f=7.1\times 10^{14}\ s^{-1}[/tex]
Let the wavelength of the light wave be [tex]\lambda[/tex].
Now, velocity of a wave is related to its frequency and wavelength as:
[tex]c=f\lambda[/tex]
Now, rewriting the above formula in terms of wavelength [tex]\lambda[/tex], we have
[tex]\lambda=\dfrac{c}{f}[/tex]
Plug in [tex]c=3\times 10^8\ m/s[/tex] and [tex]f=7.1\times 10^{14}\ s^{-1}[/tex]. Solve for [tex]\lambda[/tex]. This gives,
[tex]\lambda=\dfrac{3\times 10^8\ ms^{-1}}{7.1\times 10^{14}\ s^{-1}}\\\\\lambda=4.225\times 10^{-7}\ m[/tex]
Therefore, the wavelength of the light wave is [tex]4.225\times 10^{-7}\ m[/tex].
