Question

Two loudspeakers are located 3.50 m apart on an outdoor stage. A listener is 19.3 m from one and 20.2 m from the other. During the sound chek, 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 - 20 kHz). The speed of sound in the air is 343 m/s. What are the three lowest frequencies that give minimum signal (destructive interference) at the listener's location?

(a)  Hz (lowest)

(b)  Hz (second lowest)

(c)  Hz (third lowest)

What are the three lowest frequencies that give maximum signal (constructive interference) at the listener's location?

(d)  Hz (lowest)

(e)  Hz (second lowest)

(f)  Hz (third lowest)

Answer 1

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. Ifthis helps then kindly rate 5-stars.

Two loudspeakers are located 2.90 m apart on an outdoor stage. A listener is 18.7 m from one and 20.4 m from the other. During the sound chek, 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 - 20 kHz). The speed of sound in the air is 343 m/s. What are the three lowest frequencies that give minimum signal (destructive interference) at the listener's location?
(a) _ Hz (lowest)

(b) _ Hz (second lowest)

(c) _ Hz (third lowest)

What are the three lowest frequencies that give maximum signal (constructive interference) at the listener's location?
(d) _ Hz (lowest)

(e) _ Hz (second lowest)

(f) - Hz (third lowest)

Idea:
We have for destructive interference ?L/?=(2n-1)/2

The frequency is given as f=v/?

                                     f = (2n-1)v/2?L

here v=343 m/s and ?L=(20.4-18.7)m=1.7m

so      f=((2n-1)/2)(202 Hz)

                                

a)

the lowest frequency that gives minimum signal is for n=1

f1=((2*1-1)/2)(202 Hz)

   = 100.88 Hz

b)

The second lowest frequency that gives minimum signal is for n=2

f2 =((2*2-1)/2)(202 Hz)

   = 302.6470 Hz

c)

The thrid lowest frequency that gives minimum signal is for n=3

f3 =((2*3-1)/2)(202 Hz)

   = 504.41 Hz Hz

Idea:

Idea:
We have for constructive interference ?L/?=n

The frequency is given as f=v/?

                                     f = nv/?L

here v=343 m/s and ?L=(20.4-18.7)m=1.7m

so      f=n(202Hz)

d)

the lowest frequency that gives maximum signal is for n=1

f1= 1*(202Hz)

   = 202 Hz

e)

the second lowest frequency that gives maximum signal is for n=2

f2= 2*(202Hz)

   = 404 Hz

f)

the third lowest frequency that gives maximum signal is for n=3

f3= 3*(202Hz)

   = 606 Hz