Question

q 6. what is the frequency of a wave, if the wavelength is 3.45 x 10^14 meters? q 8.70 x 10^-7 meters q 3.90 x 10^14 meters q 1.04 x 10^23 meters q 5.67 x 10^-7 meters clear all

Explanation:

Step1: Recall wave - speed formula

The speed of light $c = \lambda
u$, where $c = 3\times10^{8}\ m/s$ (speed of light in vacuum), $\lambda$ is the wavelength and $
u$ is the frequency. We need to solve for $
u$, so $
u=\frac{c}{\lambda}$.

Step2: Substitute values

Given $\lambda = 3.45\times 10^{14}\ m$ and $c = 3\times 10^{8}\ m/s$. Then $
u=\frac{3\times 10^{8}}{3.45\times 10^{14}}$.

Step3: Calculate the frequency

Using the rule of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$, we have $
u=\frac{3}{3.45}\times10^{8 - 14}\approx0.87\times10^{- 6}=8.7\times10^{-7}\ Hz$. But the options seem to be incorrect as they are all in units of meters (wavelength units) while we are calculating frequency. If we assume it's a mistake in the options and we are actually looking for wavelength - related values, and we made a wrong start above. If we want to find a related wavelength value from the given wavelength $\lambda = 3.45\times 10^{14}\ m$, there is no clear correct operation to get one of the options. However, if we assume it's a mis - labeled frequency problem and we want to find the reciprocal - like relationship (which is not correct for this context but just to match units in options), $\frac{1}{3.45\times 10^{14}}\approx2.9\times10^{-15}\ s$. None of the options match for a correct frequency calculation or a reasonable wavelength - related calculation. But if we consider the closest in terms of magnitude and wrong - unit interpretation, we assume it's a very wrong problem setup. If we force an answer based on the wrong unit options and magnitude, we note that $\frac{1}{3.45\times10^{14}}\approx2.9\times 10^{-15}\ s$. If we consider some inverse - like operation and wrong units, the closest in magnitude among the options is $8.70\times 10^{-7}\ m$ (assuming some wrong operation was intended).

Answer:

There is an error in the problem as options are in meters (wavelength units) while we should get frequency in Hz. But if we assume some wrong operation and match magnitudes, the closest option is $8.70\times 10^{-7}\ meters$ (even though it's wrong in terms of correct physical quantity for the problem).