Final answer:
To find the angle at which the technician will observe the first minimum in sound intensity, we can use the concept of interference of waves. The formula sin(θ) = (λ/2) / (d) can be used, where θ is the angle, λ is the wavelength, and d is the width of the vertical opening. Substituting the given values, we can calculate the angle.
Step-by-step explanation:
The situation described in the question can be solved using the concept of interference of waves. When a sound wave passes through a narrow opening, it diffracts and produces a pattern of bright and dark regions called interference fringes. The first minimum in sound intensity is observed when the path difference between the two rays of sound is half a wavelength (λ/2).
To find the angle with the door at which the first minimum occurs, we can use the formula:
sin(θ) = (λ/2) / (d),
where θ is the angle, λ is the wavelength, and d is the width of the vertical opening. Rearranging the formula, we get:
θ = arcsin((λ/2) / (d)).
The wavelength (λ) can be calculated using the formula:
λ = v / f,
where v is the speed of sound and f is the frequency of the sound wave. Substituting the given values, we get:
λ = (340 m/s) / (600 Hz).
Plugging in the values into the formula for θ:
θ = arcsin(((340 m/s) / (600 Hz)) / (0.800 m)).
Calculating this gives us the angle at which the technician will observe the first minimum in sound intensity.