A transverse sinusoidal wave is generated at one end of a long, horizontal string by a bar that moves up and down through a distance of $1.00 c m$ . The motion is continuous and is repeated regularly $120$ times per second. The string has linear density $90 g m / m$ and is kept under a tension of $900 N$ . Find:
What is the transverse displacement $y$ when this maximum value of the tension occurs?

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Solution

$y = A s i n (K w - w t) \frac{d y}{d x} = s l o p e = A K c o s (K x - w t)$
as for a maximum transversesof the tension component,
the slope $\frac{d y}{d x}$ must be maximum which means
$c o s (K x - c o t) = 1 s i n (K x - c o t) = 0 ∴ y = 0$
hence transverse displacement $y = 0$ .

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y=Asin(Kw−wt)dydx=slope=AKcos(Kx−wt)as for a maximum transversesof the tension component, the slope dydx must be maximum which means cos(Kx−cot)=1sin(Kx−cot)=0∴y=0hence transverse displacement y=0.

$y = A s i n (K w - w t) \frac{d y}{d x} = s l o p e = A K c o s (K x - w t)$
as for a maximum transversesof the tension component,
the slope $\frac{d y}{d x}$ must be maximum which means
$c o s (K x - c o t) = 1 s i n (K x - c o t) = 0 ∴ y = 0$
hence transverse displacement $y = 0$ .