If the antenna is transmitting, the up-down motion of the electrons produces an electromagnetic wave with the same frequency. To increase the transmission frequency, you'd have to increase the frequency of the up-down motion, and, everything else being equal, this would take more energy. Your electric bill would go up. A standard trick that scientists use is to look at the measurement units of the quantities being multiplied. Wavelengths are distances, usually measured in meters.
Frequencies are numbers of waves per second.
That, of course, is the measurement unit of speed. In the 19th century, scientists noticed that the speed of light equals the speed of an electromagnetic wave. This was evidence that light is a form of electromagnetic wave. From this relationship of wavelength, frequency, and speed, you can calculate the wavelength for a particular frequency, or vice-versa. Just divide the frequency into the speed to get the wavelength.