Perform the following steps to verify by substitution that equations C and D are solutions to Equations A and B, respectively. a²E ax² a²E Ξερμό E = Emax cos(kx - wt) ǝt² Equation A Equation C a² B ax² = a² B B = B ερμο at² cos(kx - wt) max Equation D Equation B (a) Calculate the first partial derivatives listed below. (Use the following as necessary: k, w, x, t, and either E де дх дв дх де Ət дв at max or B max') (b) Calculate the second partial derivatives listed below. (Use the following as necessary: k, w, x, t, and either Emax or B max') a²E = 2x2 a²B ax² a²E at² a²B at² = = = (c) Given k²/w² = (1/Fλ)², calculate the ratios of the second partial derivatives below. (Use the following as necessary: c.) a²E ax2 a2E = ar2 a28 ax2 a² B at² (d) Express εolo. (Use the following as necessary: c.) Еоно

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Perform the following steps to verify by substitution that equations C and D are solutions to Equations A and B, respectively.
a²E
ax²
a²E
Ξερμό
E = Emax cos(kx - wt)
ǝt²
Equation A
Equation C
a² B
ax²
=
a² B
B = B
ερμο
at²
cos(kx - wt)
max
Equation D
Equation B
(a) Calculate the first partial derivatives listed below. (Use the following as necessary: k, w, x, t, and either E
де
дх
дв
дх
де
Ət
дв
at
max
or B max')
(b) Calculate the second partial derivatives listed below. (Use the following as necessary: k, w, x, t, and either Emax or B max')
a²E
=
2x2
a²B
ax²
a²E
at²
a²B
at²
=
=
=
Transcribed Image Text:Perform the following steps to verify by substitution that equations C and D are solutions to Equations A and B, respectively. a²E ax² a²E Ξερμό E = Emax cos(kx - wt) ǝt² Equation A Equation C a² B ax² = a² B B = B ερμο at² cos(kx - wt) max Equation D Equation B (a) Calculate the first partial derivatives listed below. (Use the following as necessary: k, w, x, t, and either E де дх дв дх де Ət дв at max or B max') (b) Calculate the second partial derivatives listed below. (Use the following as necessary: k, w, x, t, and either Emax or B max') a²E = 2x2 a²B ax² a²E at² a²B at² = = =
(c) Given k²/w² = (1/Fλ)², calculate the ratios of the second partial derivatives below. (Use the following as necessary: c.)
a²E
ax2
a2E
=
ar2
a28
ax2
a² B
at²
(d) Express εolo. (Use the following as necessary: c.)
Еоно
Transcribed Image Text:(c) Given k²/w² = (1/Fλ)², calculate the ratios of the second partial derivatives below. (Use the following as necessary: c.) a²E ax2 a2E = ar2 a28 ax2 a² B at² (d) Express εolo. (Use the following as necessary: c.) Еоно
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