The equation of a standing wave in a string fixed at both ends is given as

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Solution

$y = 2 A s i n k x c o s ω t$
$a m p l i t u d e 2 A s i n k x$
$K = \frac{2 π}{λ}$
$n o t e x i s 0$ $a n t i n o d e x = \frac{λ}{4}$
$m i d w a y x = \frac{λ}{8}$
$a m p l i t u d e = 2 A s i n (\frac{2 π}{λ}) (\frac{λ}{8})$
$= 2 A s i n \frac{π}{4}$
$= \sqrt{2} A$
$f r e q u e n c y = \frac{ω}{2 π}$

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y = (0 \cdot 4 cm) \sin [(0 \cdot 314 {cm}^{- 1}) x] \cos [(600 π s^{- 1}) t]

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