Question

Two loudspeakers (A and B) are 3.20m apart and emitting a sound with a frequency of 400Hz. An observer is 2.10m directly in front of A. If the speed of sound in this room is 340m/s will the observer hear a loud sound or a quiet sound?

Answer 1

The observer hears a loud sound

Step-by-step 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=√((3.20m)^2+(2.10m)^2)=3.827m`

Next, you calculate the wavelength of the sound waves by using the following formula:

`\lambda=(v_s)/(f)`

vs: speed of sound = 343 m/s

f: frequency of the waves = 400Hz

λ: wavelength

`\lambda=(343m/s)/(400Hz)=0.8575m`

Next, you calculate the path difference between the distance from the observer to the loudspeakers:

`\Delta d=3.827m-2.10m=1.727m`

You obtain a constructive interference (loud sound) if the quotient between the wavelength of the sound and the difference path is an integer:

`(\Delta d)/(\lambda)=(1.727m)/(0.857)\approx2`

Then, there will be a constructive interference, and the sound who the observer hears is loud.