+0  
 
0
78
1
avatar+4 

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

(please go show ALL work to get to the answer)

ARoss2  Oct 10, 2017
edited by ARoss2  Oct 10, 2017
Sort: 

1+0 Answers

 #1
avatar+18777 
+2

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

(please go show ALL work to get to the answer)

 

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

 

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

 

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

 

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

 

The wavelength of a wave is 797 nm

 

laugh

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

8 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details