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The Speed of a Wave on a String 16.3

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

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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

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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

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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

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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

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

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Oscillations (continues) Vibrating systems What we studied before? Simple harmonic motion (one mode) Mass on spring Simple pendulum (SHM for small angles)

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