Final answer:
The number of nodes and their distances in an acoustic waveguide can be calculated using the principles of standing waves, with adjustments for the medium's properties such as the speed of sound.
Step-by-step explanation:
To determine the number of nodes and their location in an acoustic waveguide (in this case, a cylindrical tube), we use the principle of a standing wave in a tube that is closed at one end and open at the other. The standing wave pattern created in such a tube consists of a node at the closed end and an antinode at the open end. Since the length of the tube is equal to ¼ of the wavelength (λ) of the standing wave, knowing the speed of sound in air at 20℃, we can calculate the wavelength using the formula λ = v/f, where v is the speed of sound and f is the frequency. For air at 20°C, the speed of sound is approximately 343 m/s. We can then determine the number of nodes from the total length available in the tube for the standing waves to form.
For helium, the process is similar but the speed of sound is different because the speed of sound in helium at the same temperature is higher, approximately 927 m/s. This affects the wavelength and consequently the number of nodes and their distance apart, as they will change with the speed of sound in the medium.