Answer:
The observer hears a loud sound
Explanation:
In order to know if the observer hears a loud or a quiet sound, you need to know if there is a constructive or destructive interference between the sound waves of the loudspeakers.
You first calculate the distance between the observer and the loudspeakers.
The distances are given by:
d1: distance to loudspeaker A = 2.10m
d2: distance to loudspeaker B
![d_2=\sqrt{(3.20m)^2+(2.10m)^2}=3.827m](https://tex.z-dn.net/?f=d_2%3D%5Csqrt%7B%283.20m%29%5E2%2B%282.10m%29%5E2%7D%3D3.827m)
Next, you calculate the wavelength of the sound waves by using the following formula:
![\lambda=\frac{v_s}{f}](https://tex.z-dn.net/?f=%5Clambda%3D%5Cfrac%7Bv_s%7D%7Bf%7D)
vs: speed of sound = 343 m/s
f: frequency of the waves = 400Hz
λ: wavelength
![\lambda=\frac{343m/s}{400Hz}=0.8575m](https://tex.z-dn.net/?f=%5Clambda%3D%5Cfrac%7B343m%2Fs%7D%7B400Hz%7D%3D0.8575m)
Next, you calculate the path difference between the distance from the observer to the loudspeakers:
![\Delta d=3.827m-2.10m=1.727m](https://tex.z-dn.net/?f=%5CDelta%20d%3D3.827m-2.10m%3D1.727m)
You obtain a constructive interference (loud sound) if the quotient between the wavelength of the sound and the difference path is an integer:
![\frac{\Delta d}{\lambda}=\frac{1.727m}{0.857}\approx2](https://tex.z-dn.net/?f=%5Cfrac%7B%5CDelta%20d%7D%7B%5Clambda%7D%3D%5Cfrac%7B1.727m%7D%7B0.857%7D%5Capprox2)
Then, there will be a constructive interference, and the sound who the observer hears is loud.