# How Do Engineers Design AntiNoise to Effectively Reduce Ambient Noise?

• Decentralized
In summary: You don't need to multiply by ##\omega##.For the first question, the value of A just needs to be a positive number that will result in a combined amplitude of 20. So it doesn't necessarily have to be 80, it could be any positive number that satisfies the equation: CombinedSound = 100 sin(ω t) + A sin(ω t + φ) = 20. For the second question, you have to consider that δ is the phase difference between the two signals, not just the phase of one of the signals. So you can set up the equation: CombinedSound = 100 sin(ω t) + 100 sin(ω t + π + δ) =
Decentralized
Summary:: AmbientNoise + AntiNoise combined calculation

I am having trouble with this question:
Noise cancelling headphones use both passive (insulated earphones) and active (electronic “anti-noise”) methods to nullify ambient noise. One task of a sound engineer is to design low-energy anti-noise signals that help cancel ambient noise. Consider anti-noise that is to be combined (to cancel) ambient-noise.

AmbientNoise = 100 sin(ω t) Amplitude 100 and frequency ω .
AntiNoise = A sin(ω t + φ) Amplitude A is a positive number. −π < φ ≤ π

1. Choose AntiNoise so the sum AmbientNoise + AntiNoise has a combined amplitude of 20 (much quieter than AmbientNoise). Guess/choose the phase φ that minimizes A (minimum A decreases hearing fatigue and energy consumption).

AmbientNoise = 100 sin(ω t)
AntiNoise = A sin(ω t + φ)
A = ____ φ = _____rad
CombinedSound = ____sin( ____ )

2. It is difficult for AntiNoise to be perfectly out of phase with AmbientNoise (i.e., difficult for φ to be exactly π). Consider AntiNoise = 100 sin(ω t + π + δ). Determine the maximum δ between 0 and π to create a combined noise/anti-noise sound of amplitude 20, i.e.,
CombinedSound = 100 sin(ω t) + 100 sin(ω t + π + δ) = 20 sin(ω t + SomePhase)
Show δ is governed by the following equation – and solve for δ.

sqr(2 − 2 cos(δ))= 0.2
δ ≈ 0.2 rad ≈ 11.5◦

For the first question, if I want to cancell ambient noise with anti noise down to 20, I am assuming it is going to be -80 sin(ω t)?
But A cannot be a negative number. I am not sure how to approach this problem. We've only learned Asin(x) + Bsin(x) = C sin(x+φ) where C = sqr( A^2 + B^2).

Decentralized said:
For the first question, if I want to cancell ambient noise with anti noise down to 20, I am assuming it is going to be -80 sin(ω t)?
But A cannot be a negative number. I am not sure how to approach this problem.
Welcome to PF.

What is the value of ##sin(\omega + \pi)## compared to ##sin(\omega)## ?

berkeman said:
Welcome to PF.

What is the value of ##sin(\omega + \pi)## compared to ##sin(\omega)## ?
Oh, It's going to be ##sin(\omega + \pi)## = ##-sin(\omega)##
Should I make it ##sin(\omega t + \pi \omega)## = ##-sin(\omega t)## so that φ = ω π, A = 80?

But if that's the case, φ depends on ω, and in the second question it gives out:
CombinedSound = 100 sin(ω t) + 100 sin(ω t + π + δ) = 20 sin(ω t + SomePhase),
in which A = 100, φ = π+ δ. It is kind of contradict with what I just got. Am I on the right direction so far?

Correct.

No, just ##sin(\omega t + \pi) = -sin(\omega t)##

## 1. What is AntiNoise Amplitude and Phase?

AntiNoise Amplitude and Phase is a technique used to reduce or eliminate unwanted noise in a signal. It involves manipulating the amplitude and phase of the noise signal in order to cancel it out.

## 2. How does AntiNoise Amplitude and Phase work?

AntiNoise Amplitude and Phase works by creating an "anti-noise" signal that is equal in amplitude but opposite in phase to the original noise signal. When these two signals are combined, they cancel each other out, resulting in a cleaner signal.

## 3. What are the applications of AntiNoise Amplitude and Phase?

AntiNoise Amplitude and Phase is commonly used in audio and video processing to reduce background noise and improve the overall quality of the signal. It is also used in medical imaging and communication systems.

## 4. How is AntiNoise Amplitude and Phase different from other noise reduction techniques?

AntiNoise Amplitude and Phase is different from other noise reduction techniques because it does not rely on filtering or removing the noise signal. Instead, it actively cancels out the noise signal, resulting in a cleaner and more accurate signal.

## 5. What are the limitations of AntiNoise Amplitude and Phase?

One limitation of AntiNoise Amplitude and Phase is that it can only cancel out noise that is constant or predictable. It may not be effective in reducing random or unpredictable noise. Additionally, it requires a reference noise signal and may not work as well in environments with multiple sources of noise.

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