The Speed of a Wave on a String

1
The Speed of a Wave on a String

• 16.3

2
Speed of a Wave

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

3
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 Newtons 2nd Law, a stronger force makes a
  quicker acceleration
• Thus, stronger tension faster wave

4
Speed of Wave in String

• Also according to Newtons 2nd Law, mass also
  affects the acceleration
• Small mass Large acceleration
• In string, the mass used is mass per unit length
  Linear Density

5
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 .401 71.27
B .708 70.68
G 1.140 71.66
D 2.333 82.33
A 4.466 88.40
E 6.790 75.48
v (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. vparticle 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

7
Practice Problems

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