Two in-phase loudspeakers separated by distance d emit 160 Hz sound waves along the x-axis. As you walk along the axis, away from the speakers, you don't hear anything even though both speakers are on.
3 Answers
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What are three possible values for d? Assume a sound speed of 340 m/s.?
Two in-phase loudspeakers separated by distance d emit 160 Hz sound waves along the x-axis. As you walk along the axis, away from the speakers, you don't hear anything even though both speakers are on
Velocity = Frequency * wave length
340 m/s = 160 cycles /s * λ m/cycle
λ m/cycle = 340 ÷ 160 =2.125 m/ cycle
The wave is 2.125 m long
If 2 waves are 180º out of phase, they will cancel each other. One wave will be compressing the air while the other wave is rarifying (expanding) the air. It would be like you standing in between 2 muscle builders. One is pushing on your chest, while the other is pushing on your back. You may feel squeezed, but you won’t move the air around you, because you won’t move.
180º out of phase is ½ a wave length out of phase. If you are 2.125 m from speaker A and 1.0625 m from the other speaker B, the wave from speaker will be at a crest when the wave from speaker B is at a trough. They will cancel each and no sound will be heard.
1.0625 m = ½ wave length
2.125 m = 1 wave length
2.125 m + 1.0625 m =
3.1875 m 1 ½ wave lengths
4.25 m = 2 wave length
4.25 m + 1.0625 m = 5.3125 2½ wave lengths
5.3125 = 2½ wave lengths
Speaker A…… Speaker B
2.125 m ………..1.0625 m…= 1 : ½
3.1875 m ………2.125 m…..= 1 ½ : 1
4.25 m …………3.1875 m…= 2 : 1 ½
5.3125 m…………4.25 m….= 2 ½ :2
In each set is the 2 speakers are 180º out phase with each other.
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electron's answer explaned the physics and the math, but missed the last bit.
put in simple terms, the speakers need to be 0.5, 1.5, 2.5 etc. (n.5) wavelengths (1.0625, 3.1875 and 5.3125 meters) apart to give you the experience.
a couple of points to note, if you are close to the speakers the volumes of the two speakers have to satisfy some definitive ratio for the sound to cancel out completely. Other wise you only get a non-zero minimum. The further away you are from them, the more closely can the volumes be equal.
walking away off the x axis you may also experience minimum but not zero because the vector nature of the vibration.
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Wavelength of 160Hz = (343/160) = 2.144m.
So 1st. possible d = (1.5 x 2.144) = 3.216m.
2nd. = ( 2.5 x 2.144) = 5.36m.
3rd = 3.5 x 2.144 = 7.504m.
