G 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

172 Hz

Explanation:

We are given that

Distance between speaker A and B=2 m

Distance between speaker B and point Q=1 m

We have to find the lowest frequency for which constructive interference occurs at point Q.

Where n=Integer

When frequency is minimum then wavelength is maximum

when n=1

Speed of sound,v=344 m/s

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west