Where Does the Intensity of Sound Waves Go in Complete Silence?

[oreo]

If we set two speakers far apart, giving identical sound waves having intensity of threshold of pain, in such a way that at midway between them, there is complete destructive interference. Would there any intensity of sound there in complete silence? If not, then where is "lost" intensity gone? Would that " silence" cause any pain?

 

[PWiz]

Intensity is the rate at which a wave transfers energy per unit area. If there is complete destructive interference midway between the speakers, then there will be no resultant wave propagation there, so the rate of energy transfer also equals 0(silence). Intensity is a relation between the characteristic properties of a wave (in this case power and area), and as such terms like "lost" do not apply to it in this case. Since the waves cancel each other midway, you can say that the air particles simply exchange some momentum and raise each other's kinetic energy of vibration over there. Whether that silence causes discomfort or not is entirely up to the listener.

 

[PWiz]

Intensity is the rate at which a wave transfers energy per unit area. If there is complete destructive interference midway between the speakers, then there will be no resultant wave propagation there, so the rate of energy transfer also equals 0(silence). Intensity is a relation between the characteristic properties of a wave (in this case power and area), and as such terms like "lost" do not apply to it in this case. Since the waves cancel each other midway, you can say that the air particles simply exchange some momentum and raise each other's kinetic energy of vibration over there. Whether that silence causes discomfort or not is entirely up to the listener.

 

[oreo]

Intensity is the rate at which a wave transfers energy per unit area. If there is complete destructive interference midway between the speakers, then there will be no resultant wave propagation there, so the rate of energy transfer also equals 0(silence). Intensity is a relation between the characteristic properties of a wave (in this case power and area), and as such terms like "lost" do not apply to it in this case. Since the waves cancel each other midway, you can say that the air particles simply exchange some momentum and raise each other's kinetic energy of vibration over there. Whether that silence causes discomfort or not is entirely up to the listener.

So if they increase each other's kinetic energy then the temperature of that area should increase! Isn't it?

 

[PWiz]

By a negligible amount, yes.

 

[oreo]

By a negligible amount, yes.

Thanks for clarification

 

[siddharth23]

If you shout for 8 years, the energy could heat up a cup of coffee. So you can imagine by how little the temperature will rise in this case.