Question

Please help! Two speakers are spaced 15 m apart and are both producing an identical sound wave. You are standing at a spot as pictured. What would be the frequency produced by the speakers to create perfectly constructive interference? Assume n = 1 and v = 343 m/s.
213.04 Hz

256.70 Hz

186.68 Hz

233.14 Hz

Answer 1

Answer:

213.04 Hz

Explanation:

Answer 2

Answer: Option (a) is the correct answer.

Explanation:

Using the Pythagoras theorem, we will calculate the the distance of $S_{1}P$ and $S_{2}P$ as follows.

        $S_{1}P = \sqrt{(10)^{2} + (22)^{2}}$

                   = 24.17

        $S_{2}P = \sqrt{(5)^{2} + (22)^{2}}$

                   = 22.56

Therefore, the path difference will be as follows.

           $\Delta r = S_{1}P - S_{2}P$

                      = 24.17 - 22.56

                      = 1.61 m

Formula for constructive interference is as follows.

                   $\Delta r = n \lambda$

                      $\lamda$ = 1.61 m      (for n = 1)  

Therefore, frequency will be calculated as follows.

                  $\nu = \frac{v}{\lambda}$

                            = $\frac{343}{1.61}$

                            = 213.043 Hz

Thus, we can conclude that frequency produced by the speakers to create perfectly constructive interference is 213.04 Hz.