91影视

The expression for the uncertainty in the wave鈥檚 position is given by,

$\mathbf{鈭�}\mathbf{x}\mathbf{鈭�}\mathbf{k}\mathbf{鈮�}\frac{\mathbf{1}}{\mathbf{2}}$

The expression for the relation between the wave number k and $\mathit{位}$is given by,$\mathit{k}\mathbf{=}\frac{\mathbf{2}\mathbf{蟺}}{\mathbf{位}}$

(a).

The wavelength$位$of the pulse is$6.33nm$.

The length $鈭�x$of the electromagnetic wave is$30cm$.

The wavenumber is calculated as,

role="math" localid="1659761406782" $$\begin{gathered} k=\frac{2\mathrm{蟺}}{位} \\ =\frac{2\mathrm{蟺}}{633nm} \\ =\frac{2\mathrm{蟺}}{633nm\left({\displaystyle \frac{{10}^{-9}m}{1nm}}\right)} \\ =9.93脳{10}^6{m}^{-1} \end{gathered}$$

The range of the wavenumber is calculated as,

$$\begin{gathered} 鈭�x鈭�k鈮�\frac{1}{2} \\ \left(30cm\left(\frac{{10}^{-2}m}{1cm}\right)\right)鈭�k鈮�\frac{1}{2} \\ 鈭�k鈮�1.67m^{-1} \end{gathered}$$

Therefore, the value of the wave number is $9.93x{10}^6{\mathrm{m}}^{-1}$and the range of the wave number is $螖k鈮�1.67m^{-1}$.

The expression for the relation between the wave numberkand$\mathit{位}$is given by,

$k=\frac{2\mathrm{蟺}}{位}$

The expression for wave equation of light is given by,

$\mathit{c}\mathbf{=}\mathit{位}\mathit{f}$

(b)

The frequency f of the pulse is 1Hz.

The expression for the wavenumber is evaluated as,

$$\begin{gathered} k=\frac{2\mathrm{蟺}}{位} \\ =\frac{2\mathrm{蟺}}{c} \\ =\frac{2\mathrm{蟺蹿}}{c} \end{gathered}$$

The value of wavenumber is calculated as,

$$\begin{gathered} k=\frac{2\mathrm{蟺蹿}}{c} \\ =\frac{2\mathrm{蟺}\left({\displaystyle \frac{1}{1\mathrm{ms}}}\right)}{3脳{10}^{8}m/s} \\ =\frac{2\mathrm{蟺}\left({\displaystyle \frac{1}{1\mathrm{ns}\left({\displaystyle \frac{1脳{10}^{-9}\mathrm{s}}{1\mathrm{ns}}}\right)}}\right)}{3脳{10}^{8}m/s} \\ =20.9m^{-1} \end{gathered}$$

The range of the wavenumber is calculated as,

$$\begin{gathered} 鈭�x鈭�k鈮�\frac{1}{2} \\ \left(30cm\left(\frac{{10}^{-2}m}{1cm}\right)\right)鈭�k鈮�\frac{1}{2} \\ 鈭�k鈮�1.67m^{-1} \end{gathered}$$

Therefore, the value of the wave number is $20.9{\mathrm{m}}^{-1}$and the range of the wave number is $鈭�k鈮�1.67m^{-1}$