complete the following frequency - problems. use the formula: 2.99792*10^8m/s = c = λ*v.\n17) a wave is…
complete the following frequency - problems. use the formula: 2.99792*10^8m/s = c = λ*v.\n17) a wave is 975nm; find its frequency.\n18) a wave is 842000000hz; find its wavelength.\n19) a wave is 500nm. whats its frequency?\n20) a 4.29*10^13hz wave has what wavelength?\n21) a wave is 450nm; find its frequency.\n22) a wave is 9.63*10^9hz; find its wavelength.\n23) a wave is 64cm; find its frequency.\n24) a wave is 8.6*10^15hz; find its wavelength.
Answer
Explanation:
Step1: Recall the wave - speed formula
The formula for the speed of a wave is $c = \lambda\nu$, where $c = 2.99792\times10^{8}\ m/s$ (speed of light in vacuum, which is used for electromagnetic waves), $\lambda$ is the wavelength and $\nu$ is the frequency. We can re - arrange it to solve for frequency $\nu=\frac{c}{\lambda}$ and for wavelength $\lambda=\frac{c}{\nu}$. 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 $\nu=\frac{c}{\lambda}=\frac{2.99792\times10^{8}\ m/s}{975\times10^{-9}\ m}\approx3.075\times 10^{14}\ Hz$.
Step3: Solve problem 18
Given $\nu = 8420000000\ Hz = 8.42\times10^{9}\ Hz$. Then $\lambda=\frac{c}{\nu}=\frac{2.99792\times10^{8}\ m/s}{8.42\times10^{9}\ Hz}\approx0.0356\ m = 3.56\ cm$.
Step4: Solve problem 19
Given $\lambda = 500\ nm = 500\times10^{-9}\ m$. Then $\nu=\frac{c}{\lambda}=\frac{2.99792\times10^{8}\ m/s}{500\times10^{-9}\ m}=5.99584\times10^{14}\ Hz\approx6.0\times10^{14}\ Hz$.
Step5: Solve problem 20
Given $\nu = 4.29\times10^{13}\ Hz$. Then $\lambda=\frac{c}{\nu}=\frac{2.99792\times10^{8}\ m/s}{4.29\times10^{13}\ Hz}\approx6.99\times10^{-6}\ m = 6990\ nm$.
Step6: Solve problem 21
Given $\lambda = 450\ nm=450\times10^{-9}\ m$. Then $\nu=\frac{c}{\lambda}=\frac{2.99792\times10^{8}\ m/s}{450\times10^{-9}\ m}\approx6.662\times10^{14}\ Hz$.
Step7: Solve problem 22
Given $\nu = 9.63\times10^{19}\ Hz$. Then $\lambda=\frac{c}{\nu}=\frac{2.99792\times10^{8}\ m/s}{9.63\times10^{19}\ Hz}\approx3.11\times10^{-12}\ m$.
Step8: Solve problem 23
Given $\lambda = 64\ cm = 0.64\ m$. Then $\nu=\frac{c}{\lambda}=\frac{2.99792\times10^{8}\ m/s}{0.64\ m}\approx4.684\times10^{8}\ Hz$.
Step9: Solve problem 24
Given $\nu = 8.6\times10^{15}\ Hz$. Then $\lambda=\frac{c}{\nu}=\frac{2.99792\times10^{8}\ m/s}{8.6\times10^{15}\ Hz}\approx3.49\times10^{-8}\ m = 34.9\ nm$.
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: $\approx34.9\ nm$