Question

y = A sin ( wt - kx ). Write the dimensions of w and k if x is distance and t is time.

Answer 1

as sin function is dimensionless and wt- kx is dimensionless
now difference of two quantity ( wt) and ( kx) is dimensionless
therefore
wt= M0L0T0
=>w* time(T1) = M0L0T0
=>w= M0L0T0 / T1= M0L0T(-1)
also
kx= M0L0T0
=>k* distance(L1) = M0L0T0
=>k= M0L0T0 /L1=M0L(-1)T0
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Answer 2

Answer:

The dimension of $w$ is $[M^{0} L^{0} T^{-1} ]$ and the dimension of k is $[M^{0} L^{-1} T^{0}]$.

Explanation:

The equation we have been given is $y = A sin (wt-kx)$

We know that the sinusoidal function is always dimensionless,

$wt-kx$ is dimensionless,

therefore, it can be written as

$wt = [M^{o} L^{0}T^{0} ]$

$w= \frac{[M^{0}L^{0}T^{0} }{[T^{1} ]}$

∴ dimension of $w = [M^{0} L^{0} T^{-1} ]$

Now, $kx = [M^{0} L^{0} T^{0} ]$

$k = \frac{[M^{0}L^{0}T^{0}] }{[L^{1} ]}$

∴ dimension of $k=[M^{0} L^{-1} T^{0} ]$

Hence, the dimension of $w$ is $[M^{0} L^{0} T^{-1} ]$ and the dimension of k is $[M^{0} L^{-1} T^{0}]$.

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