Two speaker emit the same pure tone at 170 Hz, but they are half a cycle...

Question

Question

Two speaker emit the same pure tone at 170 Hz, but they are half a cycle out of phase with each other (so one produces a tro

Answer 1

Answer #1

Wavelength of the sound wave produced by the speakers = $\lambda$ = Speed of sound / Frequency of the sound

or, $\lambda$ = 340 ( m / s ) / 170 Hz = 2 m.

So, the observer is $\lambda$ / 2 = 1 m away from one of the speakers, and, $\lambda$ = 2 m away from the other one.

Hence, path difference between the waves heard = $\lambda$ / $\lambda$ / 2 = $\lambda$ / 2.

Hence, the sounds heard is half - cycle out of phase.

Again, the sounds were initially half - cycle out of phase when produced.

So, the observer is hearing the sounds as they are in phase ( $\lambda$ / 2 + $\lambda$ / 2 = $\lambda$ ).

Hence, the observer is hearing a constructive interference, so, it will be louder than the sound produced by only one speaker.

So, correct option is : A 170 Hz tone, but if there were only one of the two speakers.

Answer 2

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