Welcome Here!!!Begin by turning in Friday’s lab (if you didn’t

already on Friday). Then remind someone around you of the similarities and differences between reflection, refraction, and diffraction.

Today’s Agenda:• Discuss Friday’s lab• Lesson: Waves on Strings• In-class practice questions• HW: Waves on Strings Worksheet

(due Wed, graded for correctness)

Learning Goal:Students will be able to predict which frequencies will resonate to produce standing waves on a given string.

Intro:• If a string is connected at one end to a

stationary clamp, and then the free end is vibrated up and down, waves begin to travel down the string, and reflect and ________ from the fixed end.

• With waves traveling in both directions, ____________ interference will happen.

• If the string is vibrated at just the right frequency, the wave will appear to stand still, so it’s called a ___________ wave.

invert

destructive

standing

Standing Waves:

Standing Waves:•The parts of the wave where complete destructive interference continually occurs are called ________, and the parts of the wave with maximum displacement are called ___________.

nodes

antinodes

Waves on Strings:• When a string is plucked, only certain

frequencies will resonate, and these frequencies are based on the _______ of the string.

• The lowest frequency to resonate is called the fundamental freq. ( f1 )

• The other resonant frequencies are called harmonics or overtones.

length

Waves on Strings:

f1 =v/1 =

v/2L

f2 = v/L =2f1

f3 =

v/(2/3)L =3f1

v/2 =

v/3 =

Example Problem:Waves travel on a 2.4m-long string at a speed of 150m/s. What are the lowest 3 frequencies that will cause this string to resonate to produce standing waves?

Group Practice Problems:1. The string in the

picture is vibrating at 330Hz. What is the fundamental frequency of this string?

2. The velocity of waves on a certain 32cm-long spring is 120m/s. Find the fundamental freq. and the 2nd and 3rd harmonics of this spring. 3. The string in the picture is vibrating at 1200Hz. If waves travel on this string at 60m/s, how long is the string?

Group Practice Problem Answers:1. 110Hz2. f1 = 187.5Hz

f2 = 275Hz

f3 = 562.5Hz

3. 0.05m