Question

Two loudspeakers are located 2.53 m apart on an outdoor stage. A listener is 21.4 m from one and 22.2 m from the other. During the sound check, a signal generator drives the two speakers in phase with the same amplitude and frequency. The transmitted frequency is swept through the audible range (20 Hz to 20 kHz). (a) What is the lowest frequency f_min,1 that gives minimum signal (destructive interference) at the listener's location? By what number must f_min,1 be multiplied to get (b) the second lowest frequency f_min,2 that gives minimum signal and (c) the third lowest frequency f_min,3 that gives minimum signal? (d) What is the lowest frequency f_max,1that gives maximum signal (constructive interference) at the listener’s location? By what number must f_max,1 be multiplied to get (e) the second lowest frequency f_max,2 that gives maximum signal and (f) the third lowest frequency f_max,3 that gives maximum signal? (Take the speed of sound to be 343 m/s.)

Answers to 3 significant digits. No scientific notation. Provide units. Thank you!

Answer 1

The two speakers are located 3.35m apart. The listener is 18.3m from one and 19.5m from the other.

Part a:

For a destructive interference

Thus,

Substitute the givens,

= 214.375 Hz

Part b :

The second lowest frequency is

  = 643.125 Hz

Part c :

The third lowest frequency is

  = 1071.875 Hz

Part d :

For a constructive interference,

Thus,

Substituting the givens

= 428.750 Hz

Part e :

The second lowest frequency

  = 857.500 Hz

Part f :

The third lowest frequency is

= 1286.250 Hz