Final answer:
The wavelength of a sound vibration with a frequency of 500 hertz, given the speed of sound in air as 1100 feet per second, is 2.2 feet.
Step-by-step explanation:
The question you've asked relates to wave mechanics, specifically the relationship between the speed of sound, frequency, and wavelength of a sound wave. This is a fundamental concept in physics, and the formula we use to connect these variables is:
v = f × λ
Where v is the speed of the wave, f is the frequency, and λ (lambda) is the wavelength. Given that the speed of sound in air is 1100 feet per second and the frequency of the sound vibration is 500 hertz (500 cycles per second), we can rearrange the formula to solve for the wavelength (λ) as follows:
λ = v / f = 1100 feet per second / 500 hertz = 2.2 feet
So, for a sound vibration with a frequency of 500 hertz, the wavelength is 2.2 feet. To explain this concept further, the wavelength is the distance between two consecutive points in the same phase of the wave, such as crest to crest or trough to trough. In this case, one cycle of the wave is 2.2 feet long.