Question

complete the following frequency - problems. use the formula: 2.9979210^8m/s = c = λv.

1. a wave is 975nm; find its frequency.
2. a wave is 842000000hz; find its wavelength.
3. a wave is 500nm. whats its frequency?
4. a 4.29*10^13hz wave has what wavelength?
5. a wave is 450nm; find its frequency.
6. a wave is 9.63*10^9hz; find its wavelength.
7. a wave is 64cm; find its frequency.
8. a wave is 8.6*10^15hz; find its wavelength.

Explanation:

Step1: Recall the wave - speed formula

The formula for the speed of a wave is $c = \lambda
u$, where $c = 2.99792\times10^{8}\ m/s$ (speed of light in vacuum, which is used for electromagnetic waves), $\lambda$ is the wavelength and $
u$ is the frequency. We can re - arrange it to solve for frequency $
u=\frac{c}{\lambda}$ and for wavelength $\lambda=\frac{c}{
u}$. Also, make sure to convert the units to SI units (meters for wavelength).

Step2: Solve problem 17

Given $\lambda = 975\ nm=975\times10^{-9}\ m$. Then $
u=\frac{c}{\lambda}=\frac{2.99792\times10^{8}\ m/s}{975\times10^{-9}\ m}\approx3.075\times 10^{14}\ Hz$.

Step3: Solve problem 18

Given $
u = 8420000000\ Hz = 8.42\times10^{9}\ Hz$. Then $\lambda=\frac{c}{
u}=\frac{2.99792\times10^{8}\ m/s}{8.42\times10^{9}\ Hz}\approx0.0356\ m = 3.56\ cm$.

Step4: Solve problem 19

Given $\lambda = 500\ nm = 500\times10^{-9}\ m$. Then $
u=\frac{c}{\lambda}=\frac{2.99792\times10^{8}\ m/s}{500\times10^{-9}\ m}=5.99584\times10^{14}\ Hz\approx6.0\times10^{14}\ Hz$.

Step5: Solve problem 20

Given $
u = 4.29\times10^{13}\ Hz$. Then $\lambda=\frac{c}{
u}=\frac{2.99792\times10^{8}\ m/s}{4.29\times10^{13}\ Hz}\approx6.99\times10^{-6}\ m = 6990\ nm$.

Step6: Solve problem 21

Given $\lambda = 450\ nm=450\times10^{-9}\ m$. Then $
u=\frac{c}{\lambda}=\frac{2.99792\times10^{8}\ m/s}{450\times10^{-9}\ m}\approx6.662\times10^{14}\ Hz$.

Step7: Solve problem 22

Given $
u = 9.63\times10^{19}\ Hz$. Then $\lambda=\frac{c}{
u}=\frac{2.99792\times10^{8}\ m/s}{9.63\times10^{19}\ Hz}\approx3.11\times10^{-12}\ m$.

Step8: Solve problem 23

Given $\lambda = 64\ cm = 0.64\ m$. Then $
u=\frac{c}{\lambda}=\frac{2.99792\times10^{8}\ m/s}{0.64\ m}\approx4.684\times10^{8}\ Hz$.

Step9: Solve problem 24

Given $
u = 8.6\times10^{15}\ Hz$. Then $\lambda=\frac{c}{
u}=\frac{2.99792\times10^{8}\ m/s}{8.6\times10^{15}\ Hz}\approx3.49\times10^{-8}\ m = 34.9\ nm$.

Answer:

17: $\approx3.075\times 10^{14}\ Hz$
18: $\approx3.56\ cm$
19: $\approx6.0\times10^{14}\ Hz$
20: $\approx6990\ nm$
21: $\approx6.662\times10^{14}\ Hz$
22: $\approx3.11\times10^{-12}\ m$
23: $\approx4.684\times10^{8}\ Hz$
24: $\approx34.9\ nm$