# The Speed of a Wave on a String 16.3. Speed of a Wave  The properties of the material determine the speed of the wave  Sound travels faster through.

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The Speed of a Wave on a String 16.3

Speed of a Wave  The properties of the material determine the speed of the wave  Sound travels faster through water, than through air

Speed of Wave in String  Wave moves through string  Each string particle is pulled up by the neighboring particle  Speed of wave is determined by how quickly a particle can be accelerated up  By Newton’s 2 nd Law, a stronger force makes a quicker acceleration  Thus, stronger tension = faster wave

Speed of Wave in String  Also according to Newton’s 2 nd Law, mass also affects the acceleration  Small mass = Large acceleration  In string, the mass used is mass per unit length = Linear Density

A Use of Speed of Wave in a String  Stringed Musical Instruments  The speed of the wave determines the pitch  The following is for a typical 6-string guitar  Find the velocities of waves in the strings m/L x10 -3 (kg/m) F(N) E.40171.27 B.70870.68 G1.14071.66 D2.33382.33 A4.46688.40 E6.79075.48v(m/s)422 316 250 188 141 105

Conceptual Example  Is the speed of the wave = to the speed of each particle on the string?  As the string vibrates back and forth, the velocity of a particle of string changes. At the maximum displacement (A), v = 0. At 0 displacement, v = maximum. v particle = A  sin  t, where  = frequency and t = time.  Velocity of wave depends on properties of string  Velocity of string particle depends on the properties of the source

Practice Problems  String out some answers to these exercises  477 CQ 5 – 7, P 12 – 17  Total of 9 Problems

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