Two loudspeakers, 5.5 m apart and facing each other, play identical sounds of the same frequency. You stand halfway between them, where there is a maximum of sound intensity. Moving from this point toward one of the speakers, you encounter a minimum of sound intensity when you have moved 0.21 m . Assume the speed of sound is 340 m/s. Part A) What is the frequency of the sound? Part B) If the frequency is then increased while you remain 0.21 m from the center, what is the first frequency for which that location will be a maximum of sound intensity? Express your answer to two significant figures and include the appropriate units. Please show ALL steps, equations AND how you get the frequency in Hz.

a)   f = 809.5 Hz ,  b)    f = 1619 Hz

Explanation:

The condition for destructive interference from the speakers is

             Δr / lam = Ф / 2π

             λ = Δr 2π / π

We substitute

            λ = 0.21 2 π/π

             Lam = 0.42 m

Now let's use the ratio of the speed of sound and the wavelength and the frequency

                v = λ f

                f = v /λ

                f = 340 / 0.42

                f = 809.5 Hz

b) in this case the intensity is maximum

         Lam = Δr 2π / 2π

          Lam = 0.21 m

          fF= v / lam

          f = 340 / 0.21

         f = 1619 Hz

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