Question

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

Answer 1

Answer:

Frequency is $213.04\ s^{-1}.$

Explanation:

Distance between source 1 from the receiver , $S_1 =\sqrt{10^2+22^2}=24.17\ m.$

Distance between source 2 from the receiver , $S_2=\sqrt{5^2+22^2}=22.56\ m.$

Now ,

Path difference , $r = S_1-S_2=24.17-22.56=1.61\ m.$

We know, for constructive interference path difference should be integral multiple of wavelength .  

Therefore, $r=n\times \lambda$

It is given that n = 1,

Therefore, $\lambda=1.61\ m.$

Frequency can be found by , $\nu=\dfrac{v}{\lambda}= \dfrac{343}{1.61}= 213.04\ s^{-1} .$

Hence, this is the required solution.