Question

Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. Consider point Q along the extension of the line connecting the speakers, 1.00 m to the right of speaker B. Both speakers emit sound waves that travel directly from the speaker to point Q. a) What is the lowest frequency for which constructive interference occurs at point Q? b) What is the lowest frequency for which destructive interference occurs at point Q?

Answer 1

Answer

a) For constructive interference, the path difference must be equal to an integer multiple of the wavelength, so

$\lambda _n = \dfrac{d}{n}$

frequency

$f_n =\dfrac{\mu}{\lambda}$

$f_n =\dfrac{\mu\ n}{d}$

$f_n =\dfrac{344\ n}{2}$

$f_n = 172\ n\ Hz$

the lowest frequency is 172 Hz. for ( n = 1)

b) Repeating the above with the path difference an odd multiple of half a wavelength,

            $f_n = ( n +\dfrac{1}{2})\times 172$

the lowest frequency is 86 Hz ( n = 0)