ShmoopTube

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And here's your sure shmoop du jour brought to you by music because [Woman sat at a desk with open books]

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without waves of sound well they're just wouldn't be music hopefully your brother

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just going through a phase with those drums a standing wave is generated by a [Girls brother playing the drums]

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string that is 24 meters long and attached to one end of a wall the

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unattached end of the string is then moved up and down to induce a wave

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motion with a total of six anti-nodes what's the wavelength of this standing

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wave and here the potential answers...All right well to answer this

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question let's take a closer look at standing waves but not too close [Girl looking at a moving string]

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it's the vibrating string and we don't want to get smacked let's imagine the same setup

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with a string anchored on the wall and us creating a wave at the other end but [Man holding a piece of string attached to a wall]

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this time we'll just send one wave down the string when the wave reaches the [One wave created down the string]

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wall it'll bounce off reflecting back down the string now if we find the right

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frequency the wave we create at one end will perfectly match the way that

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reflects off the wall when this happens we'll create a standing wave right well [A standing wave of the piece of string]

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a standing wave is created by two waves moving in opposite direction to create

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constructive interference of their points of maximum amplitude and

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destructive interference at their points of equilibrium this creates a standing

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wave which vibrates back and forth with its anti node but doesn't move at all at [Standing wave shown vibrating back and forth]

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it nodes. Well the wavelength of a standing wave equals the length of two

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complete loops formed by the nodes and antinodes. Why two? well since we're dealing

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with two waves acting in conjunction the wavelength has to include the crest and [Crest and trough of a wave]

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trough of the wave ok thanks for learning about standing waves with us

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we've certainly had a lot of fun and oh yeah we haven't answered the question. [Pieces of wood attach to spell The End]

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Well let's do some math the length of the string equals the number of anti

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nodes multiplied by the distance between each anti node and the distance between

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each antinode equals half of a wavelength so the equation looks like

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this right here now we just have to put in the numbers and solve for the [Equation for wavelength of the string]

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wavelength. A length of the string is 24 meters and we have six nodes with this

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we're able to see that the wave length equals 8 meters so the answer is B just

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remember that the wavelength in a standing wave equals the length of one wave gone [A standing wavelength]

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from equilibrium to maximum positive displacement then back to equilibrium

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down to maximum negative displacement and finally back to equilibrium phew, getting a [a rollercoaster in motion]

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little seasick here describing it like that, and if our brother keeps listening to

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the top songs of the year and at that volume well we're going to

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go in there and explain all this standing wave stuff to him in great detail [girl explaining standing waves to her brother playing the drums]

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well that should keep him quiet for a while

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