How JustAnswer Works:

  • Ask an Expert
    Experts are full of valuable knowledge and are ready to help with any question. Credentials confirmed by a Fortune 500 verification firm.
  • Get a Professional Answer
    Via email, text message, or notification as you wait on our site.
    Ask follow up questions if you need to.
  • 100% Satisfaction Guarantee
    Rate the answer you receive.

Ask Fred Your Own Question

Fred
Fred, College Student
Category: Homework
Satisfied Customers: 14
Experience:  Chemical Engineering Student
Type Your Homework Question Here...
Fred is online now
A new question is answered every 9 seconds

Why is the intensity proportional to the square of the amplitude What

Resolved Question:

Why is the intensity proportional to the square of the amplitude?

What is the concept behind this? Are we squaring the amplitude to get an area or something analogous to an area?

After the concept is explained, how does this relate to probably amplitudes (wave functions) in quantum physics?
Submitted: 5 years ago.
Category: Homework
Expert:  Fred replied 5 years ago.
Hello,

When we say that intensity is proportional to the square of the amplitude, well we are talking about RMS (root-mean square) amplitude. It is defined as the square root of the mean over time of the vertical distance (squared also) from rest state of the graph.

In other words, it is easier to use RMS than ''peak'' amplitude to calculate an intensity, because in real life, graphs do not always show a clean sinusoidal waveform. In these cases, it gets much easier to use RMS.

As an example, if you take sound waves, well these are waves that travel in the air and create a movement that is usually described as dB (decibels). This movement or displacement of the air is based on a logarithmic scale which make the intensity of the wave in the air proportional to the square of the amplitude.

Customer: replied 5 years ago.
So the intensity is like the "area" underneath the curve formed by the peak amplitude of the wave?

How does this relate to the squaring of a wave function being equal to the probability of finding a particle at a certain position at a certain time?
Expert:  Fred replied 5 years ago.
Well, RMS amplitude is not exactly the area under the graph wave, but it is like taking each point amplitude, squaring it and take the average if all points. So, if you take perfect sinusoidal wave, well, your result will be ''0'' since it goes up and down symetrical. TaXXXXX XXXXXke that, you can kind of say that it representes the area under the curve/wave.

Well, this is a postulate. I will try to explain it.
To determine where a particle is in a defined ''box'', you have to know it's ''state''. If we take normal modes, such as the classical waveform, then we can say that the probability (P) or finding a particle is :

P(x) = (A(x))^2    A : complex amplitude

Now, in quantum mechanic, the complex amplitude is also called the wave function. If you replace it you get :

P(x) = (Wave function)^2       

Hope it was clear enough, but it is not always easy to summarize these postulates.

Waiting for some feedback,

Fred
Customer: replied 5 years ago.
Well, RMS amplitude is not exactly the area under the graph wave, but it is like taking each point amplitude, squaring it and take the average if all points. So, if you take perfect sinusoidal wave, well, your result will be ''0'' since it goes up and down symetrical. TaXXXXX XXXXXke that, you can kind of say that it representes the area under the curve/wave.

For the paragraph above...at what point do you take the square root?

Can you define "box" and "state" a little differently?
Expert:  Fred replied 5 years ago.
Okay, the exact way to do it is to square the amplitude at the defined point, and then calculate the average of all the squared amplitudes.
You do not use square root, the final answer is the average of all squared amplitudes. RMS is very different from spiked amplitude, it has to be specified, but let's be honest, in real life, symetric and perfect sinusodial waveform do not exist (or almost). Therefor, almost only RMS is used to calculate intensity.

Box : it was just to define a coordinate system, or to replace the at a certain moment and place. Just use it as "environment"; or "space".

State : this is how the particle is initially placed in the "defined space" or "box". Or in generic terms, it's the initial state of the object (not taken as chemical state, but geometric (position and time) state).
Customer: replied 5 years ago.
Okay, last reply from me...let's go back to the beginning sort of


I get that you average the squared amplitudes...By why square the amplitude..what is the concept, the point of squaring the amplitude to find intensity?

Since the definition of intensity is energy per unit area and amplitude is the amount of energy at a point, then amplitude squared is the energy within that area?

In relationship to and electron,in the physical sense, [wavefunction] gives the amplitude of the wave associated with the electron. Is this amplitude a type of radius from the nucleus? And does [wavefunction]2 determines the probability of finding the moving electron in a given region or it gives the probability density. what is the given region?

Expert:  Fred replied 5 years ago.
THIS ANSWER IS LOCKED!
You can view this answer by clicking here to Register or Login and paying $3.
If you've already paid for this answer, simply Login.
Fred, College Student
Category: Homework
Satisfied Customers: 14
Experience: Chemical Engineering Student
Fred and 4 other Homework Specialists are ready to help you

JustAnswer in the News:

 
 
 
Ask-a-doc Web sites: If you've got a quick question, you can try to get an answer from sites that say they have various specialists on hand to give quick answers... Justanswer.com.
JustAnswer.com...has seen a spike since October in legal questions from readers about layoffs, unemployment and severance.
Web sites like justanswer.com/legal
...leave nothing to chance.
Traffic on JustAnswer rose 14 percent...and had nearly 400,000 page views in 30 days...inquiries related to stress, high blood pressure, drinking and heart pain jumped 33 percent.
Tory Johnson, GMA Workplace Contributor, discusses work-from-home jobs, such as JustAnswer in which verified Experts answer people’s questions.
I will tell you that...the things you have to go through to be an Expert are quite rigorous.
 
 
 

What Customers are Saying:

 
 
 
  • Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help. Mary C. Freshfield, Liverpool, UK
< Last | Next >
  • Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help. Mary C. Freshfield, Liverpool, UK
  • This expert is wonderful. They truly know what they are talking about, and they actually care about you. They really helped put my nerves at ease. Thank you so much!!!! Alex Los Angeles, CA
  • Thank you for all your help. It is nice to know that this service is here for people like myself, who need answers fast and are not sure who to consult. GP Hesperia, CA
  • I couldn't be more satisfied! This is the site I will always come to when I need a second opinion. Justin Kernersville, NC
  • Just let me say that this encounter has been entirely professional and most helpful. I liked that I could ask additional questions and get answered in a very short turn around. Esther Woodstock, NY
  • Thank you so much for taking your time and knowledge to support my concerns. Not only did you answer my questions, you even took it a step further with replying with more pertinent information I needed to know. Robin Elkton, Maryland
  • He answered my question promptly and gave me accurate, detailed information. If all of your experts are half as good, you have a great thing going here. Diane Dallas, TX
 
 
 

Meet The Experts:

 
 
 
  • Manal Elkhoshkhany

    Tutor

    Satisfied Customers:

    4520
    More than 5000 online tutoring sessions.
< Last | Next >
  • http://ww2.justanswer.com/uploads/BU/BusinessTutor/2012-2-2_115741_Kouki2.64x64.jpg Manal Elkhoshkhany's Avatar

    Manal Elkhoshkhany

    Tutor

    Satisfied Customers:

    4520
    More than 5000 online tutoring sessions.
  • http://ww2.justanswer.com/uploads/LI/lindaus/2012-6-10_04811_IMG20120609164157.64x64.jpg Linda_us's Avatar

    Linda_us

    Finance, Accounts & Homework Tutor

    Satisfied Customers:

    3121
    Post Graduate Diploma in Management (MBA)
  • http://ww2.justanswer.com/uploads/ComputersGuru/2010-02-13_051118_Photo41.JPG LogicPro's Avatar

    LogicPro

    Engineer

    Satisfied Customers:

    3035
    Expert in Java C++ C C# VB Javascript Design SQL HTML
  • http://ww2.justanswer.com/uploads/lanis/2009-4-1_233717_phput9xef_c1pm.jpg Lani S.'s Avatar

    Lani S.

    Tutor

    Satisfied Customers:

    2457
    Registered Nurse, Internet Researcher, Private Tutor
  • http://ww2.justanswer.com/uploads/chooser77/2009-08-18_162025_Chris.jpg Chris M.'s Avatar

    Chris M.

    M.S.W. Social Work

    Satisfied Customers:

    2341
    Master's Degree, strong math and writing skills, experience in one-on-one tutoring (college English)
  • http://ww2.justanswer.com/uploads/JawaadAhmed/2009-6-27_12137_SIs_SHadi.jpg F. Naz's Avatar

    F. Naz

    Chartered Accountant

    Satisfied Customers:

    1975
    Experience with chartered accountancy
  • http://ww2.justanswer.com/uploads/JK/jkcpa/2011-1-16_182614_jkcpa.64x64.jpg Bizhelp's Avatar

    Bizhelp

    CPA

    Satisfied Customers:

    1873
    Bachelors Degree and CPA with Accounting work experience