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Wave Speed

The equation ...

Question

The equation for a wave travelling in x - direction on a string is
$y = (3.0 c m) s i n [(3.14 c m^{- 1}) x - (314 s^{- 1}) t]$ Find the acceleration of a particle at x = 6.0 cm at time t = 0.11 s.

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Solution

$y = 3 c m s i n (3.14 x - 314 t)$
$a = \frac{d^{2} y}{{d t}^{2}} = - {(314)}^{2} 3 s i n (3.14 x - 314 t)$
$a t x = 6 a n d t = 0.11 s$
$a = - {(314)}^{2} 3 S i n (- 15.7)$
$a = 2355.4 c m / s^{2} = 23.5 m / s^{2}$

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Similar questions

y = (3.0 c m) s i n [(3.14 c m^{- 1}) x - (314 s^{- 1}) t]

y = (3.0 c m) s i n [(3.14 x) - (314 t)]

y = (1.0 m) sin [(3.14 c m^{- 1} \times - (157 s^{- 1}) t]

y = (1.5 c m) sin [(3.14 c m^{- 1} \times - (314 s^{- 1}) t]

x = 4.5 c m

t = 5.0 m s

Two waves passing through a region are represented by

$y = 1.0 c m s i n [(3.14 c m^{- 1}) x - (157 s^{- 1}) t]$

and $y = 1.5 c m s i n [(1.57 c m^{- 1}) x - (314 s^{- 1}) t]$

Find the displacement of the particle at x = 4.5 cm at time t = 5.0 ms.

x

y = 10 sin (π t - 0.5 x)

y

x

m

(t)

sec

x = π m

t = 1 sec

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