Final answer:
To estimate the diameter of an acoustic speaker, we can use the formula θ = λ / D, where θ is the angular spread in radians, λ is the wavelength, and D is the diameter of the speaker. Using the given values, we can calculate the estimated diameter to be approximately 0.09 meters.
Step-by-step explanation:
To estimate the diameter of an acoustic speaker, we can use the formula:
θ = λ / D
where θ is the angular spread in radians, λ is the wavelength, and D is the diameter of the speaker.
First, convert the angle from degrees to radians:
θ = 70 degrees * (pi/180 radians/degree) = 1.22 radians
Next, calculate the wavelength using the formula:
λ = v / f
where v is the speed of sound in air and f is the frequency.
λ = 330 m/s / 3000 Hz = 0.11 m
Finally, rearrange the formula for θ to solve for D:
D = λ / θ
D = 0.11 m / 1.22 radians = 0.09 m
Therefore, the estimated diameter of the acoustic speaker would be approximately 0.09 meters.