Resonance

Introduction

Resonance is the tendency of a system to oscillate with

larger amplitude at some frequencies than at others.

These are known as the system's resonant

frequencies.

At these frequencies, even small periodic driving forces

can produce large amplitude oscillations, because the

system stores vibrational energy.

Cont.,

• A complex wave can be built up out of sine waves.

• These component sine waves are called harmonics.

• The frequencies of these harmonics are always integer

multiples of the fundamental frequency of the

complex wave.

• Example: fundamental (F0) = 150 Hz

• Harmonic 1: 150 Hz

• Harmonic 2: 300 Hz

• Harmonic 3: 450 Hz, etc.

Some Notes on Music• In western music, each note is at a specific frequency

• Notes have letter names: A, B, C, D, E, F, G

• Some notes in between are called “flats” and “sharps”

261.6 Hz 440 Hz

Harmony• Notes are said to “harmonize” with each other if the greatest

common denominator of their frequencies is relatively high.

• Example: note A4 = 440 Hz

• Harmonizes well with (in order):

• A5 = 880 Hz (GCD = 440)

• E5 ~ 660 Hz (GCD = 220) (a “fifth”)

• C#5 ~ 550 Hz (GCD = 110) (a “third”)

....

• A#4 ~ 466 Hz (GCD = 2) (a “minor second”)

• A major chord: A4 - C#5 - E5

• Last time, we also learned that:

• We can represent the components of complex waves with a spectrum

• Frequency of harmonics on the x-axis

• Intensity of harmonics on the y-axis

Cont.,

• We also got the sense that vowels may be

distinguished on the basis of their spectral shapes.

Cont.,

• Last but not least, we found out that we can represent spectral

change over time with something called a spectrogram.

• time on the x-axis

• frequency on the y-axis

• intensity on the z-axis (represented by shading)

• One of the defining characteristics of speech sounds is that

they exhibit spectral change over time.

Cont.,

Fake Speech• Check out the spectrograms of our synthesized vowels:

Ch-ch-ch-ch-changes• Check out the spectrograms of some sinewaves which change in frequency over time:

Funky Stuff• Sounds that exhibit spectral change over time sound like speech, even if they’re not speech

• Example 1: sinewave speech

• Consists of three sinusoids, varying in frequency over time

Reality Check

• Note that real speech is more fleshed out, spectrally, than sinewave speech.

Funky Stuff• Sounds that exhibit spectral change over time sound like speech, even if they’re not speech

• Example 2: wah pedal

• shapes the spectral output of electrical musical instruments

Last but not least• The frequencies of harmonics are dependent on the fundamental frequency of a sound

• We cannot change the frequencies of harmonics independently of each other

• To change the spectral shape of a speech sound, we have to change the intensity of different harmonics

Resonance Examples

• Pretty much everything resonates:

• tuning forks

• bodies of musical instruments (violins, guitars, pianos)

• blowing across the mouth of a bottle

• pushing someone on a swing

• bathroom walls

• In the case of speech:

• The mouth (and sometimes, the nose) resonates in response to the complex waves created by voicing.

More on Resonance

• Objects resonate at specific frequencies, depending

on:

• What they’re made of

• Their shape

• Their size

• Think: pipe organs

• Longer, larger tubes resonate at lower frequencies.

• Shorter, smaller tubes resonate at higher

frequencies.

Traveling Waves

• How does resonance occur?

• Normally, a wave will travel through a medium indefinitely

• Such waves are known as traveling waves

Reflected Waves

• If a wave encounters resistance, however, it will be

reflected.

• What happens to the wave then depends on what kind

of resistance it encounters…

• If the wave meets a hard surface, it will get a true

“bounce”:

• Compressions (areas of high pressure) come back

as compressions

• Rarefactions (areas of low pressure) come back as

rarefactions

Sound in a Closed Tube

Wave in a closed tube

• With only one pressure pulse from the loudspeaker,

the wave will eventually dampen and die out

• What happens when:

• another pressure pulse is sent through the tube

right when the initial pressure pulse gets back to

the loudspeaker?

Standing Waves• The initial pressure peak will be reinforced

• The whole pattern will repeat itself

• Alternation between high and low pressure will continue

• ...as long as we keep sending in pulses at the right time

• This creates what is known as a standing wave.

• When this happens, the tube will vibrate in response to the motion of the standing wave inside of it.

• = it will resonate.

Resonant Frequencies

• This is important:

• a standing wave can only be set up in a tube if pressure pulses are emitted from the loudspeaker at the right frequency.

• What is the right frequency? That depends on:

• how fast the sound wave travels through the tube

• how long the tube is

• Basically:

• the longer the tube, the lower the frequency

• Why?

Establishing Resonance• A new pressure pulse should be emitted right when:

• the first pressure peak has traveled all the way down the length of the tube

• and come back to the loudspeaker.

Establishing Resonance• The longer the tube, the longer you need to wait for the pressure peak to travel the length of the tube.

• longer period between pressure pulses

• lower frequency

F0

F0

The End

….. Thank You …..