Answer:
Explanation:
Given that:
distance of the two identical loudspeakers are = 33.6 cm = 0.336 m
The frequency = 2.12 kHz = 2.12 × 10³ Hz
speed of sound V = 340 m/s
Then using the formula;
[tex]\lambda = \frac{V}{f} \\ \\ \lambda = \frac{340}{2.12*10^3} \\ \\ \lambda = 0.160 \ m[/tex]
For maximum sound intensity;
[tex]dsin \theta = m \lambda[/tex]
[tex]\theta = sin^{-1} ( \frac{m \lambda }{d})[/tex]
For m = 0
[tex]\theta_1 = sin^{-1} (\frac{0*0.160}{0.336}) \\ \\ \theta_1 = 0^0[/tex]
For m = 1
[tex]\theta_2 = sin^{-1} (\frac{1*0.160}{0.336}) \\ \\ \theta_2 = 28.44^0[/tex]
For m = 2
[tex]\theta_3 = sin^{-1} (\frac{2*0.160}{0.336}) \\ \\ \theta_3 = 72.25^0[/tex]
For m = 3
No more values for angle are found
∴ [tex]\theta_4 = \ None[/tex]
b)
For minimum intensity
[tex]dsin \theta = (m+ \frac{1}{2}) \lambda \\ \\ \\ \theta = sin^{-1} (\frac{(m+\frac{1}{2})\lambda}{d})[/tex]
For m = 0
[tex]\theta_1 = sin^{-1} (\frac{(0+\frac{1}{2})*0.160}{0.336}) \\ \\ \theta_1 = 13.77^0[/tex]
For m= 1
[tex]\theta_2 = sin^{-1} (\frac{(1+\frac{1}{2})*0.160}{0.336}) \\ \\ \theta_2 = 49.59^0[/tex]
For m = 2;
There is no value for the angle
∴ [tex]\theta_3 = 0[/tex]
