Two small speakers are driven by a common oscillator at 8.55x10^2 Hz. The speake

Question

Two small speakers are driven by a common oscillator at 8.55x10^2 Hz. The speakers face each other and are separated by d = 1.35 m. Locate the points along a line joining the two speakers where relative minima would be expected. Use v= 343 m/s. Choose one speaker as a reference and enter your answers as positive distances from this speaker from smallest to largest. Enter one in unused boxes. Two small speakers are driven by a common oscillator at 8.55x10^2 Hz. The speakers face each other and are separated by d = 1.35 m. Locate the points along a line joining the two speakers where relative minima would be expected. Use v= 343 m/s. Choose one speaker as a reference and enter your answers as positive distances from this speaker from smallest to largest. Enter one in unused boxes.

Explanation / Answer

The locations between the two speakers where destructive interference occurs,
will be locations of minimum sound levels. These location are such that the distance
from the speaker is odd multiples of half wavelength.

First, determine the wavelength of sound produced by the oscillator

lambda = c / f

= 343 / 855
  
= 0.40 m

Now set up the condition for destructive interference, letting x be the
distance of minimum sound from the arbitrarily chosen reference speaker

1.35 - x = (2*n - 1)*lambda / 2

n = 1

x = 1.35 - 0.40/2

= 1.15 m

n = 2:

x = 1.35 - 3*0.40/2

= 0.75 m

n = 3

x = 1.35 - 5*0.40/2

= 0.35 m

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