Answer:approximately 3.693 meters.
Step-by-step explanation:
To determine the wavelength of the sound wave emitted by the speakers, we can use the relationship between frequency, wavelength, and the speed of sound. The speed of sound in air is approximately 343 meters per second.
First, let's find the time delay between the two speakers due to the one-fourth period difference. The period (T) of a wave is the reciprocal of the frequency (f). Therefore, the period of the sound wave emitted by the speakers is:
T = 1 / f
T = 1 / 444 Hz
T ≈ 0.002252 seconds
Since speaker A is one-fourth of a period ahead of speaker B, the time delay between them is:
Δt = (1/4) * T
Δt ≈ 0.002252 seconds * (1/4)
Δt ≈ 0.000563 seconds
Now, let's calculate the distance traveled by the sound wave during this time delay. The speed of sound (v) is given as 343 meters per second:
Distance = Speed * Time
Distance = 343 m/s * 0.000563 s
Distance ≈ 0.193 m
Since the speakers are initially 3.50 meters apart, and the sound wave travels an additional distance of 0.193 meters, the total distance between the points where the sound waves from the speakers meet is:
Total distance = 3.50 m + 0.193 m
Total distance ≈ 3.693 m
Finally, to find the wavelength (λ) of the sound wave, we can divide the total distance by the number of wavelengths between the speakers. Since the distance between two consecutive peaks or troughs is equal to one wavelength, the number of wavelengths can be determined by dividing the total distance by the wavelength:
λ = Total distance / Number of wavelengths
λ = 3.693 m / 1
λ ≈ 3.693 m