# How to interpret this Wave Equation (Derivation) Help ?

• Shahab Mirza
In summary, the equation shows that the resultant wave function is hormonic, has the same frequency and wavelength as the individual waves, and has twice the amplitude.
Shahab Mirza
Hi dear people , Hello
I waw studying super position of two Sound Waves , traveling in same medium with same frequency , same wavelength and same amplitude while differing in phase .
quick derivation :
Wave 1 displacement y1= A sin (kx-vt ) and wave 2 displacement y2= A sin (kx-vt-phase constant)
after adding y1+y2 and then using trigonometry I got Final equation :-

y= (2A cos phase constant / 2) sin (kx-vt - phase constant / 2 ) ok now my question is that how it is interpreted in my textbook ? it is written that this equation shows that . 1. It can bee seen that resultant wave function is hormonic and has same frequency and wavelength as individual waves . Amplitude is twice than individual wave of same wavelength .

I want to know that How people interpret these equations and develop relationship between them ? I am having difficulty in physics because I lack this ability to know what equation delivers , Thanks please help me out

Shahab Mirza said:
Amplitude is twice than individual wave of same wavelength

Not always. It depends on the phase constant.

The value of cos(angle) should be 1 if the amplitude is to be 2A. If phase constant is 0,then cos0=1 and amplitude is 2A.

ash64449 said:
Not always. It depends on the phase constant.

The value of cos(angle) should be 1 if the amplitude is to be 2A. If phase constant is 0,then cos0=1 and amplitude is 2A.
Actually I used some of my efforts to understand this phenomenon on my intermediate level .
Below is what I understood .
2A (cos phase / 2) in this equation if phase is 0 then cos = 1 then amplitude is maximum means twice than individual original wave. and integral multiple of 0,2pi.3pi and so on and resulting in constructive interference.
And when if phase is pi or any odd multiple of pi ,then cos angle value = 0 and there will be minimum amplitude resulting in destructive interference.

My conclusions are :-
1: If interference is Constructive then amplitude of 1st 2nd and s one overtones/hormonics forms larger dislplacments than original individual wavelength , means if 3 waves are traveling in phase means one after other than will make 3 times larger amplitude.
2: If interference is destructive than waves will be out of phase and crest of one will fall on trough of other and there amplitudes will be equal on both sides hence cancelling each others displacement at each point .and resultant wave will have zero amplitude .

ash64449 said:
Thats good , Thanks a lot Sir

## 1. What is the wave equation and why is it important?

The wave equation is a mathematical representation of how a wave behaves. It is important because it helps us understand and predict the behavior of various types of waves, such as sound waves, light waves, and water waves.

## 2. How is the wave equation derived?

The wave equation is derived from the basic principles of wave motion, such as the principle of superposition and the conservation of energy. It is a result of combining these principles with the properties of the medium through which the wave is propagating.

## 3. What are the variables and constants in the wave equation?

The variables in the wave equation are time (t) and position (x). The constants are the speed of the wave (c) and the wavelength (λ).

## 4. Can the wave equation be applied to all types of waves?

Yes, the wave equation can be applied to all types of waves as long as they follow the basic principles of wave motion. However, the specific form of the equation may vary depending on the properties of the medium and the type of wave.

## 5. How can the wave equation be used to solve real-world problems?

The wave equation can be used to solve a variety of real-world problems, such as predicting the behavior of seismic waves in earthquakes, designing musical instruments, and understanding the properties of electromagnetic waves used in communication technology. By solving the wave equation, we can gain a better understanding of the world around us and make informed decisions in various fields of science and engineering.

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