Answer:
The shortest wavelength of an AM radio signal is 200 meters.
Step-by-step explanation:
It is given that, AM radio signals broadcast electromagnetic radiation at frequencies between 590 kHz and 1.50 MHz.
![f_1=590\ kHz=590* 10^3\ Hz](https://img.qammunity.org/2021/formulas/physics/college/c24jsh686dnlq8buyjg49py5bvtulsju7l.png)
The speed of electromagnetic wave is given by :
![c=f_1\lambda_1](https://img.qammunity.org/2021/formulas/physics/college/5ebnzqnz5authcvnj86iuw28pxc0csbed3.png)
![\lambda_1=(c)/(f_1)](https://img.qammunity.org/2021/formulas/physics/college/omc7w70m7may8i7gn281y0jbnf3zjbp1g8.png)
![\lambda_1=(3* 10^8)/(590* 10^3)](https://img.qammunity.org/2021/formulas/physics/college/ax9cn493armhcn5s6n1knjib2yxnnu08cc.png)
![\lambda_1=508.47\ m](https://img.qammunity.org/2021/formulas/physics/college/psvs384a47orwe3twkhtgiiotwgfnido7k.png)
If
![f_2=1.5\ MHz=1.5* 10^6\ Hz](https://img.qammunity.org/2021/formulas/physics/college/rk8m2humfzcjsk5ho5k5kmtzxt04n90l9y.png)
![c=f_2\lambda_2](https://img.qammunity.org/2021/formulas/physics/college/oiisc4iru1juxgz2dv9ot6j0q2u6ame75m.png)
![\lambda_2=(c)/(f_2)](https://img.qammunity.org/2021/formulas/physics/college/m4d9hnrmyl0cay14f7wwe8qhzmf8e8mcko.png)
![\lambda_2=(3* 10^8)/(1.5* 10^6)](https://img.qammunity.org/2021/formulas/physics/college/wzhgjc1pyvnw2ovyi6bbxmkqlqnnrj0can.png)
![\lambda_2=200\ m](https://img.qammunity.org/2021/formulas/physics/college/e9k55zjm8ml2a0a3mgyrejfgmwnrlczvn7.png)
So, the shortest wavelength of an AM radio signal is 200 meters. Hence, this is the required solution.