Ondas Sonoras

✹✳ ❖♥❞❛s ❙♦♥♦r❛s

✶

■♥tr♦❞✉çã♦

❉❡♣♦✐s ❞❡ t❡r♠♦s ✈✐st♦ ♣r♦♣r✐❡❞❛❞❡s ❣❡r❛✐s ❞❛s ♦♥❞❛s ✈❛♠♦s ♣❛ss❛r ❛ ❡st✉❞❛r
❛s ♦♥❞❛s ❞❡ s♦♠✳

▲❡♠❜r❡♠♦✲♥♦s ❞❡ q✉❡ ♦ s♦♠ é ✉♠❛ ♦♥❞❛ ❞❡ ❞❡♥s✐❞❛❞❡ ❞❛s

♣❛rtí❝✉❧❛s ❞♦ ♠❡✐♦ ❛tr❛✈és ❞♦ q✉❛❧ ♦ s♦♠ s❡ ♣r♦♣❛❣❛✳

❋✐❣✉r❛ ✶✿ ❖ s♦♠ é ✉♠❛ ♦♥❞❛ ❞❡ ❞❡♥s✐❞❛❞❡ ❞❛s ♣❛rtí❝✉❧❛s q✉❡ ❝♦♥st✐t✉❡♠ ♦ ♠❡✐♦
❛tr❛✈és ❞♦ q✉❛❧ ♦ s♦♠ s❡ ♣r♦♣❛❣❛✳

◆❛ ✜❣✉r❛ ❛❝✐♠❛ ✈❡♠♦s ✉♠ ♣✐stã♦ q✉❡ ♦s❝✐❧❛✱ ❡♠♣✉rr❛♥❞♦ ❛s ♠♦❧é❝✉❧❛s ❞♦ ❛r
❡ ♣r♦✈♦❝❛♥❞♦ ♦♥❞❛s ❞❡ ❞❡♥s✐❞❛❞❡ ❞❛s ♠♦❧é❝✉❧❛s ❞♦ ❛r✳

✷

❖♥❞❛s ❛✉❞í✈❡✐s✱ ✐♥❢r❛só♥✐❝❛s ❡ ✉❧tr❛só♥✐❝❛s

❆s ♦♥❞❛s s♦♥♦r❛s ❞✐✈✐❞❡♠✲s❡ ❡♠ três ❝❛t❡❣♦r✐❛s✿

•

❆s ♦♥❞❛s ❛✉❞í✈❡✐s sã♦ ❛q✉❡❧❛s q✉❡ ❝♦♥s❡❣✉✐♠♦s ♦✉✈✐r✳ ❆ s✉❛ ❢r❡q✉ê♥❝✐❛
❡stá ❝♦♠♣r❡❡♥❞✐❞❛ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ❡♥tr❡ ❛s ❢r❡q✉ê♥❝✐❛s ❞❡ ✷✵ ❍③ ❡ ✷✵
❦❍③✳

•

❆s ♦♥❞❛s ✐♥❢r❛só♥✐❝❛s tê♠ ❢r❡q✉ê♥❝✐❛s ❛❜❛✐①♦ ❞❡ ✷✵ ❍③✳ ❆s ♦♥❞❛s ❞♦s tr❡♠♦r❡s ❞❡ t❡rr❛ sã♦ ✉♠ ❡①❡♠♣❧♦ ❞❡ ♦♥❞❛s ✐♥❢r❛só♥✐❝❛s✳

✶

•

❆s ♦♥❞❛s ✉❧tr❛só♥✐❝❛s tê♠ ❢r❡q✉ê♥❝✐❛s ❛❝✐♠❛ ❞❡ ✷✵ ❦❍③✳ ❖s ♠♦r❝❡❣♦s
❝♦♥s❡❣✉❡♠ ♦✉✈✐r ❢r❡q✉ê♥❝✐❛s ❛té ✶✷✵ ❦❍③✱ ❡ ♣♦rt❛♥t♦ ♦✉✈❡♠ ♦♥❞❛s ✉❧tr❛✲ só♥✐❝❛s✱ q✉❡ ♥ós ♥ã♦ ❝♦♥s❡❣✉✐♠♦s ♦✉✈✐r✳

❆ ✜❣✉r❛ s❡❣✉✐♥t❡ ✐❧✉str❛ ❡st❡ ♣♦♥t♦

❋✐❣✉r❛ ✷✿ ❖♥❞❛s ❛✉❞í✈❡✐s✱ ✐♥❢r❛só♥✐❝❛s ❡ ✉❧tr❛só♥✐❝❛s✳

✸

❱❡❧♦❝✐❞❛❞❡ ❞❛s ♦♥❞❛s s♦♥♦r❛s

❖ ♠❡❝❛♥✐s♠♦ ❞❡ ♣r♦♣❛❣❛çã♦ ❞♦ s♦♠ é ♦ ♠❡s♠♦ ❡♠ t♦❞♦s ♦s ♠❡✐♦s✳ ❆ ✜❣✉r❛ ✶
♣♦❞❡ ❛♣❧✐❝❛r✲s❡ ❛ q✉❛❧q✉❡r ♠❡✐♦✱ só q✉❡ ❡♠ ✈❡③ ❞❡ ✉♠ ♣✐stã♦ ♣♦❞❡♠♦s ♣❡♥s❛r
♥✉♠ ♠❛rt❡❧♦ ❛ ❜❛t❡r ♥✉♠ só❧✐❞♦✱ ♣♦r ❡①❡♠♣❧♦✳

❈❧❛r♦ q✉❡ ♥✉♠ só❧✐❞♦ ♦s át♦✲

♠♦s✴♠♦❧é❝✉❧❛s ♥ã♦ tê♠ ❛ ♠❡s♠❛ ❧✐❜❡r❞❛❞❡ ❞❡ ♠♦✈✐♠❡♥t♦s q✉❡ ♥✉♠ ❣ás✳

◆♦

❡♥t❛♥t♦ é ❛✐♥❞❛ é ✈❡r❞❛❞❡ q✉❡ ♣♦❞❡♠ ♦s❝✐❧❛r ❡♠ t♦r♥♦ ❞❛ s✉❛ ♣♦s✐çã♦ ❞❡ ❡q✉✐✲
❧í❜r✐♦✳
❆ ✈❡❧♦❝✐❞❛❞❡ ❞❡ ♣r♦♣❛❣❛çã♦ ❞♦ s♦♠ ❞❡♣❡♥❞❡✱ ♥♦ ❡♥t❛♥t♦✱ ❞❛s ♣r♦♣r✐❡❞❛❞❡s
❢ís✐❝❛s ❞♦ ♠❡✐♦ ♠❛t❡r✐❛❧ ❛tr❛✈és ❞♦ q✉❛❧ s❡ ♣r♦♣❛❣❛ ♦ s♦♠✳ P♦❞❡ ♠♦str❛r✲s❡ q✉❡
❛ ✈❡❧♦❝✐❞❛❞❡ ❞♦ s♦♠ é ❞❛❞❛ ♣♦r

k
,
ρ

v=
✷

✭✶✮

❡♠ q✉❡

k

é ✉♠❛ ❝♦♥st❛♥t❡ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ ❝❛❞❛ ♠❛t❡r✐❛❧✱ q✉❡ ❞❡s❝r❡✈❡ ❛s s✉❛s

♣r♦♣r✐❡❞❛❞❡s ❡❧ást✐❝❛s✱ ❡

ρ

é ❛ ❞❡♥s✐❞❛❞❡✱
♠❛ss❛

ρ= q✉❡ t❡♠ ✉♥✐❞❛❞❡s ❞❡ ❦❣ ♠

−3

✈♦❧✉♠❡

,

✭✷✮

3
♦✉ ❦❣✴♠ ✳

◆♦ ❝❛s♦ ❞♦s ❣❛s❡s ❡ ❞♦s ❧íq✉✐❞♦s✱

k é ♦ ♠ó❞✉❧♦ ✈♦❧✉♠étr✐❝♦
B