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# Wavelength Problem

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What is the wavelength of a wave having a frequency of 3.76 multiplied by 10^14 s^-1?

ARoss2  Oct 10, 2017
edited by ARoss2  Oct 10, 2017
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What is the wavelength of a wave having a frequency of 3.76 multiplied by 10^14 s^-1?

$$\begin{array}{llll} \text{Here is the formula of the wavelength } (\lambda) \\ \text{depending on } v (\text{velocity of the wave }) \text{ and } f (\text{frequency}). \\ \end{array}$$

$$\begin{array}{rrr} && \mathbf{\lambda = \dfrac{v}{f} } \\ \end{array}$$

$$\begin{array}{llll} \mathbf{\lambda} & \text{ (Lambda) is the wavelength } \\ \mathbf{v} & \text{ is the velocity of the wave (default is velocity of light in vacuum: } 299792458 \frac{m}{s} ) \\ \mathbf{f} & \text{ is the frequency } \\ \end{array}$$

$$\begin{array}{|rcll|} \hline \lambda &=& \dfrac{v}{f} \quad & | \quad v=299792458 \frac{m}{s} \qquad f = 3.76\ \cdot 10^{14} \frac{1}{s} \\\\ &=& \dfrac{299792458 \frac{m}{s}} {3.76\ \cdot 10^{14} \frac{1}{s}} \\\\ &=& \dfrac{299792458 } {3.76\ \cdot 10^{14} } \cdot \frac{m}{s} \cdot \frac{s}{1} \\\\ &=& \dfrac{299792458 } {3.76\ \cdot 10^{14} } \ m \\\\ &=& \dfrac{2997.92458\cdot 10^{5} } {3.76\ \cdot 10^{14} } \ m \\\\ &=& \dfrac{2997.92458} {3.76}\cdot 10^{5-14} \ m \\\\ &=& \dfrac{2997.92458} {3.76}\cdot 10^{-9} \ m \quad & | \quad nm = 10^{-9} \ m \\\\ &=& \dfrac{2997.92458} {3.76}\ nm \\\\ &\mathbf{=}& \mathbf{797.320367021 \ nm} \\ \hline \end{array}$$

The wavelength of a wave is 797 nm

heureka  Oct 11, 2017
edited by heureka  Oct 11, 2017