# L05_a - Transverse Wave on a String Wave speed depends on...

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Transverse Wave on a String Wave speed depends on properties of medium: For a string, will see µ / T v = o T is string tension o is mass/unit length (i.e. linear density) to see, apply 2 nd law to element of string (red) in frame moving left with crest at speed v o In this frame: string element s near crest moves around circular arc of radius R (don’t actually know R )

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Define θ as half of angle subtended by arc s of radius R : o Properties of string element are then: ± Length: 2 × = R s ± Mass: µ 2 × × = R m Force on element is due to tension T at ends o Radial component of force is T T F 2 sin 2 R = for small (in radians) Centripetal acceleration of element is R v a / 2 cent = Newton’s 2 nd law says cent R a m F = o So: R v R T / 2 2 2 × × × =
Cancel θ and R (didn’t know anyway) to get µ / T v = o Says: for wave on string, 2 v : ± Increases with tension tighter string, faster wave ± Decreases with linear density

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L05_a - Transverse Wave on a String Wave speed depends on...

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