Superposition of Waves-2 : Stationary (Standing) Waves : Vibration of Air Columns

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A bounded medium is one which has definite boundaries and whose boundaries are separated from other media by distinct surfaces. It vibrates with only certain definite frequencies called characteristic…

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Stationary waves are formed when a wave reflects from a boundary and superposes with an identical wave moving in the opposite direction. Without boundaries, reflection does not occur, so stationary wa…

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A wave reflected from a free or open end does not suffer any phase change. The reflected wave is y=a sin ((2 pi)/(lambda) (v t+x)).

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A wave reflected from a rigid or closed end suffers a phase change of pi or 180 degrees. The reflected wave is y=-a sin ((2 pi)/(lambda) (v t+x)).

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Given: amplitude a = 2 cm. Rule for free end reflection: y = a sin ((2 pi)/(lambda) (v t+x)). The amplitude remains the same, so the reflected wave amplitude is 2 cm. No phase change occurs at the fre…

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Given: amplitude a = 3 cm. Rule for rigid end reflection: y = -a sin ((2 pi)/(lambda) (v t+x)). Amplitude = 3 cm. Phase change = pi radians = 180 degrees. The negative sign shows the inversion on refl…

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The stationary wave equation is y=-2 a sin ((2 pi x)/(lambda)) cos ((2 pi t)/(T)). Here T = lambda/v. The displacement is zero at nodes and maximum at antinodes.

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The stationary wave equation is y=2 a cos ((2 pi x)/(lambda)) sin ((2 pi t)/(T)). Here T is the period. This form shows nodes and antinodes fixed in space.