Tentukan persamaan percepatan gelombang pada gelombang berjalan

Tentukan persamaan percepatan gelombang pada gelombang berjalan

Jawaban yang benar adalah a = -Aω² sin (ωt – kx) dengan a dalam m/s².

Gelombang merambat yang selalu memiliki amplitudo tetap disebut gelombang berjalan.

Secara umum, persamaan simpangan gelombang berjalan adalah sebagai berikut :
y = A sin (ωt – kx)
dengan :
y = simpangan gelombang (m)
A = Amplitudo gelombang (m)
ω = kecepatan sudut (rad/s)
t = lama titik asal bergetar (s)
k = bilangan gelombang (1/m)
x = jarak titik sembarang dari titik asal (m)

Persamaan kecepatan partikel di suatu titik merupakan turunan pertama simpangan terhadap waktu.
v = dy/dt
v = Aω cos (ωt – kx)
dengan :
v = kecepatan partikel di suatu titik (m/s)

Persamaan percepatan gelombang merupakan turunan dari kecepatan terhadap waktu.
a = dv/dt
a = -Aω² sin (ωt – kx)
dengan :
a = percepatan gelombang (m/s²)

Jadi persamaan percepatan gelombang pada gelombang berjalan adalah a = -Aω² sin (ωt – kx) dengan a dalam m/s²

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