True noise cancelling headphones are more expensive than traditional noise absorbing headphones.
True noise cancelling headphones uses the concept of destructive interference of sound waves to cancel the noise from the surroundings.
The outer noise can be interpreted as a usual signal which can be decomposed into superposition of multiple sines and cosine signals. If a sound containing similar frequency is emitted from headphones with a lag of half the wavelength, the signals will destructively interfere causing no sound to enter the user's ears thereby cancelling the outer noise. This component which in real-time sends out the signal to cancel the noise is what makes these headphones expensive than the regular noise absorbing headphones.
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