Answer to Question #250047 in Mechanics | Relativity for John

Question

Convert the following frequencies to wavelengths (please present the final answer in the most appropriate units to present the quantities in a succinct manner):

a. 10.37 Hz

b. 400.1 MHz

c. 1.91 GHz

d. 79 GHz

e. 167 MHz

Answer 1

We know from the start that $c=3 \times 10^8\,m/s=\lambda \cdot \nu \implies \lambda=\cfrac{c}{\nu}$. Then we start to calculate the values as it follows

a. 10.37 Hz $\implies \lambda_a=\cfrac{3 \times 10^8\,m/s}{10.37\,Hz}\cdot \cfrac{1\,Hz}{1\,s^{-1}}=2.893\times 10^{7}\,m=289.3\,nm$

b. 400.1 MHz $\implies \lambda_b=\cfrac{3 \times 10^8\,m/s}{400.1\,MHz}\cdot \cfrac{1\,MHz}{10^6\,s^{-1}}=0.750\,m$

c. 1.91 GHz $\implies \lambda_c=\cfrac{3 \times 10^8\,m/s}{1.91\,GHz}\cdot \cfrac{1\,GHz}{10^9\,s^{-1}}=0.157\,m$

d. 79 GHz $\implies \lambda_d=\cfrac{3 \times 10^8\,m/s}{79\,GHz}\cdot \cfrac{1\,GHz}{10^9\,s^{-1}}=3.797\times 10^{-3}\,m=3.797\, mm$

e. 167 MHz $\implies \lambda_e=\cfrac{3 \times 10^8\,m/s}{167\,MHz}\cdot \cfrac{1\,MHz}{10^6\,s^{-1}}=1.796\,m$

Reference:

• Sears, F. W., & Zemansky, M. W. (1973). University physics.