Velocity from Wave Solution

Classical Mechanics Level 1

What is the velocity (in appropriate units) of a traveling wave described by the equation:

y ( x , t ) = sin ⁡ ( 4 x − 2 t + π ) ? y(x,t) = \sin(4x - 2t + \pi)\:\:\:?

1 2 \frac12 4 4 2 2 1 1

Matt DeCross by Matt DeCross , 27, USA

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3 solutions

Renjie Cui
Jan 1, 2018

L a T e X LaTeX y(x,t)= sin(4x-2t+Pi)= sin( 4(x-1/2) +pi) therefore the velocity is 1/2

1 Helpful 0 Interesting 0 Brilliant 1 Confused
Prasit Sarapee
Sep 2, 2016

k(x-vt)=4x-2t = 4(x-1/2t) --> v=1/2

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ankith A Das
Mar 13, 2016

v = ω k T h i s c a n b e d e r i v e d f r o m v = ϑ λ ω = 2 π ϑ a n d k = 2 π λ ω = 2 a n d k = 4 S o v = 1 2 v=\frac { \omega }{ k } \\ This\quad can\quad be\quad derived\quad from\quad v=\vartheta \lambda \quad \\ \omega =2\pi \vartheta \quad and\quad k=\frac { 2\pi }{ \lambda } \\ \omega =2\quad and\quad k=4\\ So\quad v=\frac { 1 }{ 2 }

1 Helpful 0 Interesting 0 Brilliant 0 Confused

velocity is a vector, so why shouldn't the answer be -1/2 ?

xx xx - 4 months ago

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