Question

what is
is the dimentional formula of
ø from the following relaion
y = A sin (øt - ax)​

Answer 1

Explanation:

 In the equation y = A sin (ω− Kx), obtain the dimensional formula of ω and K. Given x is distance and t is time.

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Answer 2

Answer: [M°L°T°]

Given:

$\sf y=A\:sin(\phi-ax)$

To find:

$\sf The\:dimensional\:formula\:of\:\phi .$

Explanation:

$\sf The\:powers\:of\:fundamental\:quantities\:which\:are\:raised\:to\:represent\:unit\\\:is\:called\:Dimensional\:formula.$

$\sf We\:know\:that,$

$\sf sin\:is\:a\:trigonometry\:function,hence\:it\:is\:a\:dimensionless\:quantity.\\If\:sin\:a\:dimensionless\:quantity,\therefore\:(\phi-ax)\:will\:also\:become\:dimensionless\:as\:it\:is\:an\:angle.$

$\therefore \sf (\phi-ax)=1$

$\Rightarrow \boxed{\sf \phi=1=[M^{\circ}L^{\circ}T^{\circ}]}$

Hence,Φ is a dimensionless quantity i.e.[M°L°T°].