To calculate the phase difference in sound sensation based on the difference in distance between the right and left human ears, we need to use the formula:
Phase Difference = (2π / λ) * Δx
Where:
- Phase Difference is the phase difference in radians
- λ (lambda) is the wavelength of the sound wave
- Δx is the difference in distance between the ears
First, let's calculate the wavelength (λ) of the sound wave using the formula:
λ = v / f
Where:
- v is the speed of sound in air (approximately 343 meters per second at room temperature)
- f is the frequency of the tone
Given that the frequency (f) is 1000 Hz, we can calculate the wavelength:
λ = 343 m/s / 1000 Hz = 0.343 meters = 34.3 cm
Now we can calculate the phase difference:
Phase Difference = (2π / λ) * Δx
Plugging in the values: Δx = 1 cm = 0.01 meters
Phase Difference = (2π / 0.343 meters) * 0.01 meters Phase Difference ≈ 0.183 radians
Therefore, for a tone with a frequency of 1000 Hz and a 1 cm difference in sound wave distance between the right and left human ears, the phase difference in sound sensation is approximately 0.183 radians.