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Introductory Physics Homework Help
Superposition of two one-dimensional harmonic waves
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[QUOTE="orangephysik, post: 6867580, member: 734442"] [B]Homework Statement:[/B] (See below) [B]Relevant Equations:[/B] (See below) ##\mathbf {Homework ~Statement:}## Consider the superposition of two one-dimensional harmonic waves $$s_1(x,t)=3.5 cm \cdot cos(27.5s^{-1} \cdot t - 5.65m^{-1} \cdot x)$$ $$s_2(x,t)=3.5 cm \cdot cos(27.5s^{-1} \cdot t - 5.5m^{-1} \cdot x)$$ ##\mathbf {a)}## Calculate the wavelength ##\lambda##, the propagation speed ##v## and the period ##T## for both waves ##\mathbf {b)}## Calculate the superposition ##s(x,t)## of both waves ##\mathbf {c)}## For which ##x_{max}## will the amplitude be a maximum? What are these values? ##\mathbf {Relevant ~Equation:}## ##cos(\alpha)+cos(\beta) = 2 \cdot cos(\frac{\alpha + \beta}{2}) \cdot cos(\frac{\alpha - \beta}{2})## -------------------------------------------------------------------------------------------------------------- ##\mathbf {Attempt ~at~ a ~Solution:}## ##\mathbf {a)}## Well the equations are in the form of ##u(x,t) = a \cdot cos(\omega t \mp kx)##, whereby ##|k| = \frac{2\pi}{\lambda} = \frac{\omega}{v}## and ##\omega = 2\pi f=\frac{2\pi}{T}## I get [TABLE] [TR] [TD][/TD] [TD]##\lambda##[/TD] [TD]##v##[/TD] [TD]##T##[/TD] [/TR] [TR] [TD]##s_1(x,t)##[/TD] [TD]##1.11m##[/TD] [TD]##4.86 m/s##[/TD] [TD]##0.228 s##[/TD] [/TR] [TR] [TD]##s_2(x,t)##[/TD] [TD]##1.14m##[/TD] [TD]##4.99 m/s##[/TD] [TD]##0.228 s##[/TD] [/TR] [/TABLE] ##\mathbf {b)}## Using the relevant equation I got ##s_1 + s_2 =## ## 7 cm \cdot cos(\frac{55s^{-1}\cdot t-11.15 m^{-1}\cdot x}{2})cos(0.075)## ##\mathbf {c)}## I considered the case for ##cos(0)=cos(\pi)=1## and got ##x=\frac{55s^{-1}\cdot t}{11.15 m^{-1}}## and ##x=-\frac{2\pi - 55s^{-1}\cdot t}{11.15 m^{-1}}## and so the maximum amplitude would then be ##x_{max}=\pm 7cm\cdot cos(0.075)## Are my solutions correct? I remember for part (a) I got 0 points in the exam. I don't know what I did wrong. [/QUOTE]
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Introductory Physics Homework Help
Superposition of two one-dimensional harmonic waves
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