The document discusses the speed of waves on a string. It provides an equation that shows the speed depends on the tension force (F) and the mass per unit length (μ) of the string. To slow a pulse moving along a string, students could loosen the tension or use a heavier string, as both would decrease the speed according to the equation.

1. Harmonic WavesHarmonic 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.