Suppose a wave of visible light of wavelength equal to 555nm was traveling at a velocity of 55.5 cm/s past a point "A". How long would it take for one wavelength of the light to travel past the point "A"?

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Answer:

The answer is "[tex]1 \times 10^{-6}\ s[/tex]"

Explanation:

[tex]v = velocity = 55.5 \ \frac{cm}{s} = 55.5 \times 10^{-2} \ \frac{m}{s}\\\\\lambda = wavelength = 555 \ nm = 555 \times 10^{-9}\ m\\\\\upsilon = frequency\\\\v = \lambda \upsilon \\\\\upsilon = \frac{v}{ \lambda}\\\\[/tex]

[tex]\upsilon= 55.5 \times 10^{-2} \ \frac{m}{s} \div 555 \times 10^{-9}\ m\\\\\ \ \ \ \ = \frac{10^6}{s}[/tex]

In 1 second, [tex]10^6[/tex] cycles take place.

1 wavelength cycle included. Thus, [tex]10^6[/tex] cycles include [tex]10^6[/tex] wavelengths.

[tex]10^6[/tex] wavelengths 1 second until point A [tex]10^6[/tex]

1 wavelength is [tex]\frac{1}{10^6}\ sec = 10^{-6}[/tex]seconds after A.