Final answer:
The wavelength of a sound wave at 400 Hz in 20°C air is approximately 0.8575 meters, calculated using the speed of sound (343 m/s) and the formula λ = Vw/f.
Step-by-step explanation:
To answer the question of finding the closest wavelength of a sound wave with a frequency of 400 Hz in 20°C air, we can use the formula for wave speed: Vw = fλ, where Vw is the speed of sound, f is the frequency, and λ (lambda) is the wavelength. We know the speed of sound in air at 20°C is approximately 343 meters per second (m/s).
To find the wavelength (λ), we rearrange the formula to λ = Vw/f. Substituting the known values, we get λ = 343 m/s ÷ 400 Hz, which equals about 0.8575 meters. Therefore, the closest wavelength of a sound wave at 400 Hz in 20°C air is approximately 0.8575 meters.