Speaker A is at (x,y) = (1.0 m, 2.0 m) and Speaker B is at (-2.0 m, 1.0 m). Both

Question

Speaker A is at (x,y) = (1.0 m, 2.0 m) and Speaker B is at (-2.0 m, 1.0 m). Both of these speakers radiate sound uniformly in all directions in air at 20°C. The speakers are in phase and the acoustic power output from each of the speakers is the same. The wavelength of the sound is = 4.0 m . The pressure amplitude at the origin is 0.029 Pa if one of the speakers is turned on. (a) Find the pressure amplitude at a point (x,y) = (-2.0 m, -2.0 m) if only speaker A is turned on. (b) Find the pressure amplitude at a point (x,y) = (-2.0 m, -2.0 m) if only speaker B is turned on. (c) Find the pressure amplitude at the origin if both speakers are turned on. (d) Find the pressure amplitude at a point (x,y) = (-2.0 m, -2.0 m) both speakers are turned on.

Explanation / Answer

a) distance between point A and at (x,y)= sqrt{ (-2-1)2 + (-2-2)2 } = 5 m ; take as Ra=5

distance between point A and the origin(Ro)= sqrt{ (1-0)2 + (2-0)2 } = sqrt(5);

Amplitude is inversely proportional to R2

So, ampliude at the point (A1) *Ra2 =Ao*Ro2

A1= 0.0058 Pa

b. distance between the point nd point B (Rb) = sqrt{ (-2+2)2 + (-2-1)2 } = 9 m

as before, ampliude at the point (A2) *Rb2 =Ao*Ro2

A2= 0.016 Pa

c. distance form both A and B to the origin is same. So the phase shift between A and B at the origin is same.

Implies that constructive interference is occured

So, pressure amplitude at origin= Ao + Ao =0.029 + 0.029 =0.058 Pa

d. phase shift(p)= (R/ L)*2*pi ; L=wave length and D-distance travelled

For A, R=Ra ; L=4; p1= 2.5*pi

for B, R=Rb ; L=4; p2= 1.5*pi

phase difference of A adn B at the point= p1-p2 = pi

waves get destructive interference;

Amplitude= A2- A1= 0.0102 Pa

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.