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

Frequency is
`213.04\ s^(-1).`

Step-by-step explanation:

Distance between source 1 from the receiver ,
`S_1 =√(10^2+22^2)=24.17\ m.`

Distance between source 2 from the receiver ,
`S_2=√(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* \lambda`

It is given that n = 1,

Therefore,
`\lambda=1.61\ m.`

Frequency can be found by ,
`\\u=(v)/(\lambda)= (343)/(1.61)= 213.04\ s^(-1) .`

Hence, this is the required solution.