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Show that the equation
MATHEMATICS · Subjective · ISC · Mathematics · Physics · Calculus
Problem
Show that the equation,
y
=
a
sin
(
ω
t
−
k
x
)
y = a \sin (\omega t - kx)
y
=
a
sin
(
ω
t
−
k
x
)
satisfies the wave equation
∂
2
y
∂
t
2
=
v
2
∂
2
y
∂
x
2
\frac{\partial^2 y}{\partial t^2} = v^2 \frac{\partial^2 y}{\partial x^2}
∂
t
2
∂
2
y
=
v
2
∂
x
2
∂
2
y
. Find speed of wave and the direction in which it is travelling.
Related theory
Differentiation Rules
Higher-Order Derivatives
Waves
Second-order derivatives
Frequency period and angular frequency
Displacement relation in a progressive wave
Derivatives of composite functions
Basic concepts of differential equations
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