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Standing Wave Visualization

A generator a...

Question

A generator at one end of a very long string creates a wave given by
$y = (6.0 c m) cos \frac{π}{2} [(2.00 m^{- 1}) x + (8.00 s^{- 1}) t]$
and a generator at the other end creates the wave
$y = (6.0 c m) cos \frac{π}{2} [(2.00 m^{- 1}) x - (8.00 s^{- 1}) t]$
For $x \geq 0,$ what is the location of the antinode having the third smallest value of x?

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Solution

The displacement is a maximum where $cos (k x) = \pm 1 .$
This means $k x = n π,$ where $n$ is an integer.
Thus, $x = n (1.00 m) .$
The third smallest value of $x$ that corresponds to an anti-node (maximum) is
$x = 2.00 m (n = 2)$

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Similar questions

y_{1} = (6.0 c m) cos \frac{π}{2} [(2.00 m^{- 1}) x + (8.00 s^{- 1}) t]

y_{2} = (6.0 c m) cos \frac{π}{2} [(2.00 m^{- 1}) x - (8.00 s^{- 1}) t]

x > 0

c m

x

x = 0 and x = L

y = (0.8 c m) sin [(0.314 c m - 1) x] cos [(600 π s^{- 1}

The equation of a standing wave, produced on a string fixed at both ends, is $y = (0.4 c m) s i n [(0.314 c m^{- 1}) x] c o s [(600 π s^{- 1}) t]$

What could be the smallest length of the string?

1

2

2

9

1

x = 0

y_{i} = (3 cm) cos [(3.14 {cm}^{- 1}) x - (314 {rad s}^{- 1}) t]

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