Final answer:
Waves with a frequency of 1.25 x 10⁹ Hz have a high number of cycles per second, a short wavelength, and are typically in the electromagnetic spectrum, beyond the range of human hearing.
Step-by-step explanation:
The student's question asks for a description of the characteristics of waves with a frequency of f = 1.25 × 10⁹ Hz.
Firstly, the frequency (f) of a wave indicates how many cycles of the wave occur in one second and is measured in hertz (Hz), which corresponds to cycles per second. A frequency of 1.25 × 10⁹ Hz means that 1.25 billion cycles occur every second. This type of high-frequency wave can be found in certain types of electromagnetic radiation, such as microwaves or radio waves, depending on the exact frequency.
Secondly, the wavelength (λ) of a wave, which is the distance between two consecutive crests or troughs, is inversely proportional to frequency. This means that waves with higher frequencies have shorter wavelengths. Therefore, waves with a frequency of 1.25 × 10⁹ Hz will have relatively short wavelengths, potentially on the order of mere centimeters or less, common for microwave frequency ranges.
Lastly, this high frequency is well beyond the range of human hearing, which typically falls between 20 Hz and 20 kHz. These waves would require specialized electronic equipment to detect and measure.