Two loudspeakers are located 3.0 m apart on the stage of an auditorium. A listener at point P is seated 19.0 m from one speaker and 15.0 m from the other. A signal generator drives the speakers in phase with the same amplitude and frequency. The wave amplitude at P due to each speaker alone is A. The frequency is then varied between 30 Hz and 400 Hz. The speed of sound is 343 m/s.
-Determine the value of the maximum amplitude in terms of A.
A)2.0A
B)2.5A
C)3.0A
D)4.0A
E)5.0A

Question

Two loudspeakers are located 3.0 m apart on the stage of an auditorium.  A listener at point P is seated 19.0 m from one speaker and 15.0 m from the other.  A signal generator drives the speakers in phase with the same amplitude and frequency.  The wave amplitude at P due to each speaker alone is A.  The frequency is then varied between 30 Hz and 400 Hz.  The speed of sound is 343 m/s.
-Determine the value of the maximum amplitude in terms of A.
A)2.0A
B)2.5A
C)3.0A
D)4.0A
E)5.0A

Quizplus · Accepted Answer

The maximum amplitude occurs when the waves from the two speakers arrive at point P in phase, which means they constructively interfere. Constructive interference happens when the path difference between the waves is an integer multiple of the wavelength, leading to a phase difference of $2\pi n$ (where $n$ is an integer). The amplitude of the resultant wave at point P is the sum of the amplitudes of the individual waves, which is $A + A = 2A$ in this case, since the problem states that the wave amplitude at P due to each speaker alone is $A$.

Two Loudspeakers Are Located 3