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Physics
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10 Nov 2019

1. Use the classical wave equation (Helmholtz equation) to showthat the superposition of two one-dimensional harmonic waves y =y(x,t), one traveling to right and the other one traveling to theleft is a wavefunctions that represents a classical wave that couldpossibly exist in nature. What does the superposition of these twowaves actually represent?




I am just not sure how to set this problem up. I know I canuse:
y1=Asin(kx-ωt)

y2=Bsin(kx+ωt)

Y=y1+y2

I just do not understand what is being asked of me?? Pleasehelp.

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Sixta Kovacek
Sixta KovacekLv2
10 Nov 2019
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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

A string of mass .03 kg and length 2 m is fixed at one end, anddriven with an oscillator at the other end. The oscillator inducestraveling waves on the string of the form
y=A sin (kx-(omega)t) which traveled down the string, hit the fixedend, and get reflected back as a wave with the form y=Asin(kx+(omega)t).
I'm asked to find the a.) velocity of the waves, b.)frequencyrequired to generate a wave with 4 nodes, and c.) derive a generalequation for standing waves on a string using the two aboveequations.

So I have: m = 0.03 kg and L = 2 m
a.) I have a lot of equations, such as
(lambda) = 2L = 4 m
k = 2(pi)/(lambda) = (pi)/2
µ = m/L = 0.015 kg/m
,but all the equations I know to find velocity involve eithertension or frequency or another variable that I don't have. How doI find the velocity with what I'm given?

b.) I think that 4 nodes is the 2nd harmonic frequency (?) wheren=2 in the equation
f = n * (v/2L). Is this right? If so, I can easily find it when Ihave the answer for velocity.

c.) I think that for this part, I just add the two equationstogether. I'd call one y1 and the other y2. y1 + y2 = generalequation?
[sin a + sin ß = 2 sin ((a+ß)/2) cos ((a-ß)/2)]

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