Constructive and destructive waves with equal amplitudes?

[hongiddong]

1. If two wave lengths have the same amplitude and have the exact same phase(360 degrees, 0 degrees, or 2pi) and is constructive, will the amplitude double?

2. If two wave lengths have the same amplitude and are exactly out of phase(180 degrees, pi) will the resultant wave have a straight line?

 

[phinds]

What do YOU think will happen? What is your reasoning?

In this forum, we try to help folks figure out how to solve problems. We don't spoon feed answers.

And by the way, this is a homework type problem so you are supposed to use the homework template. Please read the forum rules.

 

[hongiddong]

Ooo, ok I get it I get it. My reasoning is that since, the amplitudes subtract and add depending on if it is constructive or destructive and also on the phase of the two wave; therefore, my answer is correct. However, I now have another question due to thinking about this.

How does 2 waves become superimposed on to each other? For a situation with a rope, besides standing wave, can we have two people wiggling the rope to get two different waves on the same rope that creates a super imposed resultant wave? How do we superimpose a wave for sounds and light?

Thank you!

 

[phinds]

Ooo, ok I get it I get it. My reasoning is that since, the amplitudes subtract and add depending on if it is constructive or destructive and also on the phase of the two wave; therefore, my answer is correct. However, I now have another question due to thinking about this.

Yep.

How does 2 waves become superimposed on to each other? For a situation with a rope, besides standing wave, can we have two people wiggling the rope to get two different waves on the same rope that creates a super imposed resultant wave? How do we superimpose a wave for sounds and light?

Superposition of sound waves and waves in an electric signal are done by having a source that produces two or more frequencies at the same time. Your vocal chords do this very nicely, as do musical instruments.

In electronics, Fourier Analysis shows us that an ideal square wave is actually the superposition of an infinite number of sine waves.

 

[CWatters]

How does 2 waves become superimposed on to each other? For a situation with a rope, besides standing wave, can we have two people wiggling the rope to get two different waves on the same rope that creates a super imposed resultant wave?

Indeed. If two people send identical pulses down a rope from each end the pulses will meet in the middle and become superimposed on each other at that point. I couldn't actually find a youtube vid that showed it on a rope but it looks something like this..



PS Ignore the sound track on this vid it has nothing to do with anything.

How do we superimpose a wave for sounds and light?

Any time you send two sound waves through the same space they superimpose where they meet (which is typically everywhere). For example if you listen to two sound sources (eg from stereo speakers) the sound waves are superimposed at your ear. You may not be aware of it but you are hearing a complex mix of constructive and destructive interference that changes all the time.

You only hear obvious constructive or destructive interference if you play something simple like a pure tone from both speakers and then move your head around.

 

[anorlunda]

You should also think of noise cancelling headphones. They deliberately produce waves tuned to interfere destructively with the noise waves. They aren't perfect, but they do a pretty good job.

 

[hongiddong]

ahh thank you everyone!

 

[sophiecentaur]

You should also think of noise cancelling headphones. They deliberately produce waves tuned to interfere destructively with the noise waves. They aren't perfect, but they do a pretty good job.

Sound cancellation (or cancellation of any waves) can only happen in certain regions and will always result in enhancement in others. The energy always has to end up somewhere. You can force a Null in one place and the energy will turn up somewhere else. You may manage to produce a good null in your ear canal with sound cancelling earphones but someone next to you may well hear things louder. (I think I have said the same thing twice -but the message is important.

 

[phinds]

Sound cancellation (or cancellation of any waves) can only happen in certain regions and will always result in enhancement in others. The energy always has to end up somewhere. You can force a Null in one place and the energy will turn up somewhere else. You may manage to produce a good null in your ear canal with sound cancelling earphones but someone next to you may well hear things louder. (I think I have said the same thing twice -but the message is important.

That has most emphatically not been my experience. My wife has a set of Bose noise cancelling headphones and when she had them on I hear absolutely nothing from them regardless of how she turns her head or moves closer or farther away. And I know from wearing them that they do a great job of cancelling almost all (but not all) of the ambient noise.

 

[Bobbywhy]

1. If two wave lengths have the same amplitude and have the exact same phase(360 degrees, 0 degrees, or 2pi) and is constructive, will the amplitude double?

2. If two wave lengths have the same amplitude and are exactly out of phase(180 degrees, pi) will the resultant wave have a straight line?

hongiddong,

You may visit this website and find clear answers to your questions.

http://www.physicsclassroom.com/class/waves/Lesson-3/Interference-of-Waves

Cheers, Bobbywhy

 

[sophiecentaur]

That has most emphatically not been my experience. My wife has a set of Bose noise cancelling headphones and when she had them on I hear absolutely nothing from them regardless of how she turns her head or moves closer or farther away. And I know from wearing them that they do a great job of cancelling almost all (but not all) of the ambient noise.

But how would you actually measure the increase in sound level? You would be trying to detect the small amount of sound energy that would have been entering the ear space of the phones, spread around the region outside them. That would be totally swamped, subjectively, by the sound that is arriving. How could you differentiate between the noises around you and the small amount of noise the phones are chucking out?

You must always apply basic principles in these matters and not go looking for 'exceptions' to what Physics tells you. Energy cannot just disappear.