Speakers

When two waves meet their amplitudes add.

Constructive interference—the two waves add to make a wave of greater amplitude.

Destructive interference—the two waves are opposite in amplitude and cancel each other out.

Connecting Speakers In-Phase

Out-of-Phase Speakers

Active sound cancellation

In-Phase, Different Distance

Tap your fingers on your desk

What happens when a pulse hits the end and turns around? Does it return on the same side of the

rope or does it invert?

Reflection

Standing Waves Two sine waves in different directions

Reflections– Slinky– Periodic laser potentials

sin (𝑘𝑥−𝜔𝑡 )+sin (𝑘𝑥+𝜔𝑡 )=2 cos (𝜔𝑡 ) sin (𝑘𝑥)

3 2 1 1 2 3

2

1

1

2

In the standing wave shown, what is its wavelength?

In the standing wave shown, what is the amplitude?

the points which oscillate with the most amplitude are called antinodes

10 cm

1 meter

123 Q8-3

What is the wavelength of the wave which is generatingthe standing wave shown below?

(a) L/3(b) 2L/3(c) L

LUKE 16:1-13

PARABLE OF THE UNJUST STEWARD

Resonance, Harmonics

Jigsaw Standing Wave Demo

J15-3

Consider a 3-loop standing wave on an elastic cord.If I increase the tension in the cord, the velocity of the waves in the cord will

(a) increase,(b) decrease, or(c) remain the same.

If I unhook and pull on the belt, I get A. more loops

B. fewer loopsC. does not change the

number of loops

T

v

f

v

fv

The sound you hear from a violin is produced by . . .

1. The string—determines the pitch (frequency)

2. The violin body—couples sound to the air

3. The bow—provides the energy—

driver

ResonanceWhen you push a Swing does it

make a difference when you push?

Tacoma Narrows Bridge http://www.youtube.com/watch?v=xox9BVSu7Ok

Violin The fundamental frequency or 1st

harmonic (the lowest frequency for that length) determines the ________ you hear.

The 2nd harmonic frequency is twice the frequency of the first harmonic – a violinist can remove the fundamental by lightly touching the string at the half way point and you hear the 2nd harmonic.

pitch

For a finite string (a violin string, for example), to change the fundamental frequency you

can change . . . 1. the length of the string. 2. the mass per unit length of the

string. 3. the tension in the string.

You hear a violinist playing a series of notes by moving their fingers up the fingerboard to effectively reduce the length of the string. As she does this, the notes you hear . . .

A. become higher in pitchB. become higher in pitchC. stays the same pitch

You hear a violinist playing a series of notes by moving their fingers up the fingerboard to effectively reduce the length of the string. As she does this, the wave speed . . . A. DecreasesB. IncreasesC. Stays the same

A string fastened at both ends has a length of 1.0 m. Two possible wavelengths for standing waves are

A. 4 m and 2 mB. 2 m and .5 mC. 3 m and .5 mD. 4 m and 1 mE. 3 m and 2 m

http://www.youtube.com/watch?v=CR6t47pV8Qc

Victor Wooten guitar