Question

As shown in the figure, Two Loudspeakers are located at point A and B. Both are vibrating in phase at a frequency f and $P_1$ and $P_2$ are their respective power outputs. Point C lies on a line joining the two loudspeakers at a distance of $d_1$ from A and $d_2$ from B. Take velocity of sound = 300ms–1, frequency $f=100Hz.d_1=1m$ and $d_2=1.5m.P_1=8\pi$ watts and $P_2=18\pi$ watts. Also, assume that loudspeakers behave like point isotropic sources. (emit sound uniformly in all directions).With both speakers switched on, the intensity (in W/m2) at point___

Answer 1

Path difference $=\Delta x=d_2-d_2=0.5$

$\varphi =\frac{2\pi }{\lambda }.\Delta x=\frac{2\pi f}{v}\Delta x=2\pi \times \frac{100}{300}.\frac{1}{2}=\frac{\pi }{3}$

Intensity at C:

$I=I_1+I_2+2\sqrt{I_1{I}_2}cos\varphi$

$=\frac{P_1}{4\pi d_1^2}+\frac{P_1}{4\pi d_2^2}+\frac{2}{4\pi d_1{d}_2}\sqrt{P_1{P}_2}cos\left(\frac{\pi }{3}\right)=6W/m^2$