Question

Two speakers face each other, and they each emit a sound of wavelength λ. One speaker is 180∘ out of phase with respect to the other. If we separate the speakers by a distance 1.5λ, how far from the left-most speaker should we place a microphone in order to pick up the loudest sound? Ignore reflections from nearby surfaces. Select all that apply.a. 3/4λb. 0 λc. 1/2λd. 1/4λe. 1 λ

Answer 1

a. 3/4λ

d. 1/4λ

Step-by-step explanation:

When the wavelength of the sound waves is λ and the two waves are having same frequency the waves are said to be out of phase if their phase difference is in the multiples of
`(\lambda)/(2)` or 180°.

When the two waves are out of phase then their opposite maxima coincide at the same time resulting in the minimum amplitude of the resulting wave throughout.

• As we observe from the schematic that the a wave has sinusoidal pattern of variation and we get a maxima after each
  `(\lambda)/(4)` of the distance.

• Here we have two speakers out of phase therefore on shifting one of the speakers by the odd multiples of
  `(\lambda)/(2)` we have the maxima or the extreme amplitudes.

So, we must place the microphone at 3/4λ and 1/4λ to pickup the loudest sound.