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Harmonic WavesHarmonic Waves
2
The speed of a wave on a string
• When a portion of a string under tension is displaced, a wave will be
launched along the string.
• It is probably not surprising that the velocity will depend on the
tension force F and on the weight of the string (actually the
mass/unit length µ). Think of a guitar whose strings are all at the
same tension. The thicker strings will produce a lower tone due to
the slower speed of the wave (we will discuss standing waves
shortly).
• Here is the expression for the propagation speed:
3
• Example : Two children are playing with a string that is fixed at
one end. By moving their hand up and down they can generate a
wave pulse. They want to take a picture of it, but it's too fast. How
can they make the pulse move slower?
• (choose ALL that apply)
• They could move their hands up and down a larger distance as they
generate the pulse.
• They could loosen the string tension.
• They could tighten the string tension.
• They could move their hand up and down slower.
• They could use a heavier string.
• They could use a lighter string.
4
 According to the formula depends on F(Ts) andAccording to the formula depends on F(Ts) and µ.µ.
 Μορεοϖερ, µ=Μ/ΛΜορεοϖερ, µ=Μ/Λ
 1.Ιν ορδερ το σλοω τηε σπεεδ οφ τηε πυλσε, τηε στρινγ τενσιον1.Ιν ορδερ το σλοω τηε σπεεδ οφ τηε πυλσε, τηε στρινγ τενσιον
Τσ σηουλδ δεχρεασεσ, σο ς δεχρεασεσ.Τσ σηουλδ δεχρεασεσ, σο ς δεχρεασεσ.
 2 Τηε σπεεδ οφ τηε πυλσε αλσο δεπενδσ ον µ, ωηεν µ ισ2 Τηε σπεεδ οφ τηε πυλσε αλσο δεπενδσ ον µ, ωηεν µ ισ
ραισεδ, συχη ασ ωε υσε α ηεαϖιερ στρινγ, τηε σπεεδ οφ τηεραισεδ, συχη ασ ωε υσε α ηεαϖιερ στρινγ, τηε σπεεδ οφ τηε
πυλσε ωουλδ βε λοωερ.πυλσε ωουλδ βε λοωερ.
 σο τηε χορρεχτ ανσωερ σηουλδ βε τηε σεχονδ ονε ανδ τηεσο τηε χορρεχτ ανσωερ σηουλδ βε τηε σεχονδ ονε ανδ τηε
φιφτη ονε.φιφτη ονε.

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Harmonic Waves

  • 2. 2 The speed of a wave on a string • When a portion of a string under tension is displaced, a wave will be launched along the string. • It is probably not surprising that the velocity will depend on the tension force F and on the weight of the string (actually the mass/unit length µ). Think of a guitar whose strings are all at the same tension. The thicker strings will produce a lower tone due to the slower speed of the wave (we will discuss standing waves shortly). • Here is the expression for the propagation speed:
  • 3. 3 • Example : Two children are playing with a string that is fixed at one end. By moving their hand up and down they can generate a wave pulse. They want to take a picture of it, but it's too fast. How can they make the pulse move slower? • (choose ALL that apply) • They could move their hands up and down a larger distance as they generate the pulse. • They could loosen the string tension. • They could tighten the string tension. • They could move their hand up and down slower. • They could use a heavier string. • They could use a lighter string.
  • 4. 4  According to the formula depends on F(Ts) andAccording to the formula depends on F(Ts) and µ.µ.  Μορεοϖερ, µ=Μ/ΛΜορεοϖερ, µ=Μ/Λ  1.Ιν ορδερ το σλοω τηε σπεεδ οφ τηε πυλσε, τηε στρινγ τενσιον1.Ιν ορδερ το σλοω τηε σπεεδ οφ τηε πυλσε, τηε στρινγ τενσιον Τσ σηουλδ δεχρεασεσ, σο ς δεχρεασεσ.Τσ σηουλδ δεχρεασεσ, σο ς δεχρεασεσ.  2 Τηε σπεεδ οφ τηε πυλσε αλσο δεπενδσ ον µ, ωηεν µ ισ2 Τηε σπεεδ οφ τηε πυλσε αλσο δεπενδσ ον µ, ωηεν µ ισ ραισεδ, συχη ασ ωε υσε α ηεαϖιερ στρινγ, τηε σπεεδ οφ τηεραισεδ, συχη ασ ωε υσε α ηεαϖιερ στρινγ, τηε σπεεδ οφ τηε πυλσε ωουλδ βε λοωερ.πυλσε ωουλδ βε λοωερ.  σο τηε χορρεχτ ανσωερ σηουλδ βε τηε σεχονδ ονε ανδ τηεσο τηε χορρεχτ ανσωερ σηουλδ βε τηε σεχονδ ονε ανδ τηε φιφτη ονε.φιφτη ονε.