In a certain home sound system, two small speakers are located so that one is 60
ID: 2227259 • Letter: I
Question
In a certain home sound system, two small speakers are located so that one is 60.0 cm closer to the listener than the other. A.) For what frequencies of audible sound will these speakers produce destructive interference at the listener? (Find only the three lowest audible frequencies.) If there is more than one value, separate your answers with commas. B.) For what frequencies of audible sound will these speakers produce constructive interference at the listener? (Find only the three lowest audible frequencies). If there is more than one value, separate your answers with commas .Explanation / Answer
The speed of sound at sea level is 343.2 meters/second. A wavelength of 70 cm occurs at a frequency of 486 Hz.
A.) For what frequencies of audible sound will these speakers produce destructive interference at the listener? (Find only the three lowest audible frequencies.) If there is more than one value, separate your answers with commas
Therefore, a constructive phase relationship would occur at 486 Hz because one speaker would be precisely one full cycle "behind" the other, and no canceling would occur (IOW, both signals at the listener's position would be moving positive at the same time, albeit one full cycle out of phase).
B.) For what frequencies of audible sound will these speakers produce constructive interference at the listener? (Find only the three lowest audible frequencies). However, for a frequency that has a wavelength where the 70 cm phase shift would cause a 180 degree shift in the sound wave, such as one that equals 70 + 35 cm (i.e. 324 Hz), canceling would occur because one signal will be moving positive while the other will be moving in a negative direction at the listener's position.
It might be easier to envision this if you draw a diagram and show the signals as sine waves with their wavelengths drawn to scale.