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- https://query.libretexts.org/Idioma_Portugues/Fisica_Universitaria_I_-_Mecanica_Som_Oscilacoes_e_Ondas_(OpenStax)/18%3A_Chave_de_resposta_para_problemas_selecionados/18.16%3A_Ondas125. \[\begin{split} \frac{\partial^{2} (y_{1} + y_{2})}{\partial t^{2}} & = -A \omega^{2} \sin (kx - \omega t) - A \omega^{2} \sin (kx - \omega t + \phi) \\ \frac{\partial^{2} (y_{1} + y_{2})}{\parti...125. \[\begin{split} \frac{\partial^{2} (y_{1} + y_{2})}{\partial t^{2}} & = -A \omega^{2} \sin (kx - \omega t) - A \omega^{2} \sin (kx - \omega t + \phi) \\ \frac{\partial^{2} (y_{1} + y_{2})}{\partial x^{2}} & = -Ak^{2} \sin (kx - \omega t) - Ak^{2} \sin (kx - \omega t + \phi) \\ \frac{\partial^{2} y(x,t)}{\partial x^{2}} & = \frac{1}{v^{2}} \frac{\partial^{2} y(x,t)}{\partial t^{2}} \\ -A \omega^{2} \sin (kx - \omega t) - A \omega^{2} \sin (kx - \omega t + \phi) & = \left(\dfrac{1}{v^{2}}\ri…
- https://query.libretexts.org/%D8%A7%D9%84%D9%84%D8%BA%D8%A9_%D8%A7%D9%84%D8%B9%D8%B1%D8%A8%D9%8A%D8%A9/-_____(OpenStax)/18%3A_%D9%85%D9%81%D8%AA%D8%A7%D8%AD_%D8%A7%D9%84%D8%A5%D8%AC%D8%A7%D8%A8%D8%A9_%D8%B9%D9%84%D9%89_%D8%A7%D9%84%D9%85%D8%B4%D8%A7%D9%83%D9%84_%D8%A7%D9%84%D9%85%D8%AD%D8%AF%D8%AF%D8%A9/18.16%3A_%D8%A7%D9%84%D8%A3%D9%85%D9%88%D8%A7%D8%AC147. \[\begin{split} \sin(kx - \omega t) & = \sin \left(kx + \dfrac{\phi}{2}\right) \cos \left(\omega t + \dfrac{\phi}{2}\right) - \cos \left(kx + \dfrac{\phi}{2}\right) \sin \left(\omega t + \dfrac{\...147. \[\begin{split} \sin(kx - \omega t) & = \sin \left(kx + \dfrac{\phi}{2}\right) \cos \left(\omega t + \dfrac{\phi}{2}\right) - \cos \left(kx + \dfrac{\phi}{2}\right) \sin \left(\omega t + \dfrac{\phi}{2}\right) \\ \sin(kx - \omega t + \phi) & = \sin \left(kx + \dfrac{\phi}{2}\right) \cos \left(\omega t + \dfrac{\phi}{2}\right) + \cos \left(kx + \dfrac{\phi}{2}\right) \sin \left(\omega t + \dfrac{\phi}{2}\right) \\ \sin(kx - \omega t) + \sin(kx - \omega t + \phi) & = 2 \sin \left(kx + \dfrac…
- https://query.libretexts.org/%E7%AE%80%E4%BD%93%E4%B8%AD%E6%96%87/%E5%A4%A7%E5%AD%A6%E7%89%A9%E7%90%86%E5%AD%A6_I-%E5%8A%9B%E5%AD%A6%E3%80%81%E5%A3%B0%E9%9F%B3%E3%80%81%E6%8C%AF%E8%8D%A1%E5%92%8C%E6%B3%A2%E6%B5%AA_(OpenStax)/18%3A_18%EF%BC%9A%E9%80%89%E5%AE%9A%E9%97%AE%E9%A2%98%E7%9A%84%E7%AD%94%E6%A1%88%E5%85%B3%E9%94%AE/18.16%3A_18.16%EF%BC%9AWaves147。 \[\begin{split} \sin(kx - \omega t) & = \sin \left(kx + \dfrac{\phi}{2}\right) \cos \left(\omega t + \dfrac{\phi}{2}\right) - \cos \left(kx + \dfrac{\phi}{2}\right) \sin \left(\omega t + \dfrac{\...147。 \[\begin{split} \sin(kx - \omega t) & = \sin \left(kx + \dfrac{\phi}{2}\right) \cos \left(\omega t + \dfrac{\phi}{2}\right) - \cos \left(kx + \dfrac{\phi}{2}\right) \sin \left(\omega t + \dfrac{\phi}{2}\right) \\ \sin(kx - \omega t + \phi) & = \sin \left(kx + \dfrac{\phi}{2}\right) \cos \left(\omega t + \dfrac{\phi}{2}\right) + \cos \left(kx + \dfrac{\phi}{2}\right) \sin \left(\omega t + \dfrac{\phi}{2}\right) \\ \sin(kx - \omega t) + \sin(kx - \omega t + \phi) & = 2 \sin \left(kx + \dfrac…
- https://query.libretexts.org/Kiswahili/Chuo_Kikuu_Fizikia_I_-_Mitambo%2C_Sauti%2C_oscillations%2C_na_Waves_(OpenStax)/18%3A_Jibu_muhimu_kwa_Matatizo_Yaliyochaguliwa/18.16%3A_Mawimbi147. \[\begin{split} \sin(kx - \omega t) & = \sin \left(kx + \dfrac{\phi}{2}\right) \cos \left(\omega t + \dfrac{\phi}{2}\right) - \cos \left(kx + \dfrac{\phi}{2}\right) \sin \left(\omega t + \dfrac{\...147. \[\begin{split} \sin(kx - \omega t) & = \sin \left(kx + \dfrac{\phi}{2}\right) \cos \left(\omega t + \dfrac{\phi}{2}\right) - \cos \left(kx + \dfrac{\phi}{2}\right) \sin \left(\omega t + \dfrac{\phi}{2}\right) \\ \sin(kx - \omega t + \phi) & = \sin \left(kx + \dfrac{\phi}{2}\right) \cos \left(\omega t + \dfrac{\phi}{2}\right) + \cos \left(kx + \dfrac{\phi}{2}\right) \sin \left(\omega t + \dfrac{\phi}{2}\right) \\ \sin(kx - \omega t) + \sin(kx - \omega t + \phi) & = 2 \sin \left(kx + \dfrac…
- https://query.libretexts.org/Francais/Physique_universitaire_I_-_M%C3%A9canique%2C_son%2C_oscillations_et_ondes_(OpenStax)/18%3A_La_cl%C3%A9_de_r%C3%A9ponse_%C3%A0_certains_probl%C3%A8mes/18.16%3A_Ondes147. \[\begin{split} \sin(kx - \omega t) & = \sin \left(kx + \dfrac{\phi}{2}\right) \cos \left(\omega t + \dfrac{\phi}{2}\right) - \cos \left(kx + \dfrac{\phi}{2}\right) \sin \left(\omega t + \dfrac{\...147. \[\begin{split} \sin(kx - \omega t) & = \sin \left(kx + \dfrac{\phi}{2}\right) \cos \left(\omega t + \dfrac{\phi}{2}\right) - \cos \left(kx + \dfrac{\phi}{2}\right) \sin \left(\omega t + \dfrac{\phi}{2}\right) \\ \sin(kx - \omega t + \phi) & = \sin \left(kx + \dfrac{\phi}{2}\right) \cos \left(\omega t + \dfrac{\phi}{2}\right) + \cos \left(kx + \dfrac{\phi}{2}\right) \sin \left(\omega t + \dfrac{\phi}{2}\right) \\ \sin(kx - \omega t) + \sin(kx - \omega t + \phi) & = 2 \sin \left(kx + \dfrac…