Final answer:
The angular position of the first minimum in the diffraction pattern of 600-nm light passing through a 1.0 m wide doorway is 7.32 × 10^-4 radians. The angular position of the first minimum in the diffraction pattern of a musical note of frequency 440 Hz passing through the same doorway is 267.5235 radians.
Step-by-step explanation:
To find the angular position of the first minimum in the diffraction pattern of 600-nm light passing through a doorway of width 1.0 m, we can use the formula 0 = 1.22 * λ / D, where λ is the wavelength of the light and D is the width of the aperture.
For 600-nm light, the angular position of the first minimum can be calculated as follows:
0 = 1.22 * (600 * 10^-9 m) / 1.0 m = 7.32 × 10^-4 radians.
For a musical note of frequency 440 Hz, we can use the formula 0 = λ / D * v, where λ is the wavelength of the sound, D is the width of the aperture, and v is the speed of sound.
First, we need to calculate the wavelength of the sound using the formula λ = v / f, where f is the frequency of the sound:
λ = (343 m/s) / 440 Hz = 0.7805 m.
Then, we can calculate the angular position of the first minimum:
0 = (0.7805 m) / 1.0 m * (343 m/s) = 0.7805 * 343 = 267.5235 radians.