To solve this problem we will apply the concepts related to Frequency (Reverse to Period) and the description of the wavelength as a function of the speed of light at the rate of frequency.
Our Laser frequency is given as
[tex]f = 9*10^{14}Hz[/tex]
Therefore the laser wavelength would be
[tex]\lambda = \frac{c}{f}[/tex]
Where,
c = Speed of light
f = Frequency
[tex]\lambda = \frac{3*10^8}{ 9*10^{14}}[/tex]
[tex]\lambda = 3.33*10^{-7}[/tex]
The laser pulse is emitted at a period (T) of [tex]8.8*10^{-6}s[/tex]
Therefore the pulse wavelength would be
[tex]\lambda' = \frac{c}{f}[/tex]
[tex]\lambda' = c \frac{1}{f} \rightarrow \frac{1}{f} = T[/tex]
[tex]\lambda' = c *T[/tex]
[tex]\lambda' = (3*10^8)(8.8*10^{-6})[/tex]
[tex]\lambda' = 2640m[/tex]
Finally the number of wavelengths is the ratio between the two wavelengths, then
[tex]n = \frac{\lambda'}{\lambda}[/tex]
[tex]n = \frac{2640}{3.33*10^{-7} }[/tex]
[tex]n = 7.927*10^9[/tex]
The number of wavelengths in the beam length is closer to [tex]7.927*10^9[/tex]
