Final answer:
The shortest wavelength that can be heard at a frequency of 15,000 Hz is approximately 0.02293 meters or 2.293 centimeters, calculated using the wave speed formula with the speed of sound at 344 m/s.
Step-by-step explanation:
The question asks to determine the shortest wavelength audible to humans, assuming the highest frequency that can be heard is 15,000 Hz and knowing that sound waves have different properties such as frequency and wavelength. The speed of sound in air at typical room temperature (20°C) is approximately 344 meters per second (m/s). Using the formula for wave speed (v=fλ, where v is velocity, f is frequency, and λ is wavelength), we can calculate the shortest wavelength (λ) that can be heard based on the highest audible frequency.
For a frequency (f) of 15,000 Hz, we would calculate the wavelength (λ) as follows:
λ = v / f
λ = 344 m/s / 15,000 Hz
λ = 0.02293 meters
Therefore, the shortest wavelength that can be heard at 15,000 Hz is approximately 0.02293 meters or about 2.293 centimeters.