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physique ondulatoire, Exercises of Particle Physics

Université Ibn Zohr AgadirParticle Physics
Prof. Lahcen Talb

On appelle onde toute grandeur physique, (scalaire ou vectorielle) qui dépende à la fois des coordonnées d’espace et du temps, et qui est solution d’une équation différentielle aux dérivés partielles, couplant ses variables (d’espace et du temps), appelé équation d’onde.

Typology: Exercises

2022/2023

Uploaded on 05/05/2023

outalb
outalb 🇲🇦

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6) Application numérique : pour le fer, on trouve : o 7,35.10" Hz et ic = 5820ms" 1 Su =— a\m Rq: cette vitesse est typique de la propagation des ondes sonores dans les solides ; quant ala fréquence maximum, il s’agit bien sir d’ultrasons: on parle méme de « la célérité des ondes est identique = la relation de dispersion que l'on obtiendrait a partir de I’équation de D’Alembert 7 oO” " a (ke =—) montre que tous les vecteurs d’ondes ont la méme norme ; compte-tenu du sens de k. ke, et k=ké, propagation, il vient : r On en déduit ; |u’(t)=rAexp[i(-kna—ot)]]} et ui (t) = tAexp[i(kna —ot)] c) Outre la relation (3), il faut trouver un deuxiéme lien entre r ett ; appliquons la du relation (1) a l’atome de masse mM, = Mo a =a(u_,—2y +m) Or: w,=u, tu, =Aewe™ 41x dee su sul=txdeMe™ 5 uy =uy=txde™ ; d’od: —meo't =a(e™ +re™ —21+1te™)=—m, sin’ (ka /2)t =a[-2i sin(ka) — 24(1 e"*)] - = — m | sin /2)-( -coska—isinka) |. =Fsinka ; il vient finalement : m 0 1 : t=te rr avec : i 1 (™ 1)tan{ £) m 2 e) Cas particuliers : 0 — il est logique de ne pas obtenir d’onde réfléchie, puisque onde #m,o=m: t=letr run «défaut » du réseau cristallin. incidente n’est pas « perturbée » en x=0 pa