Complex Waves

Question 1

A sine wave is:

Waves that are NOT sinusoidal are:

Answer 1

The fundamental component of all other sound waves

Complex waves

Question 2

Any wave that is not a sinusoid is a:

Answer 2

Complex wave

Question 3

Complex waves consist of:

Answer 3

A series of simple sinusoids

Question 4

Complex waves consisting of a series of simple sinusoids can differ in what 3 things?

Answer 4

Frequency

Amplitude

Phase

Question 5

When complex waves are decomposed you can determine what?

Answer 5

The amplitudes, frequencies, and phases of the sinusoidal components

Question 6

ALL complex waves can be classified by reference to:

Answer 6

1. Is periodicity present?

2. How complex is the wave?

Question 7

Name 3 important examples of periodic waves:

Answer 7

1. Sine wave (periodic but NOT complex)
2. Sawtooth wave
3. Square wave

Question 8

What are periodic waves?

Answer 8

Waves repeat themselves over time.

They have “harmonic relation”

Question 9

What is harmonic relation:

Answer 9

Each sinusoid in the series must be an integer multiple of the lowest in the component series:

Ex. 1000, 2000, 3000 etc.

Question 10

Give example of the first 4 harmonics in a series if:

The fundamental frequency is 125Hz

Answer 10

125

250

375

500

Question 11

Define square wave:

Answer 11

“Progressive summation of 4 components with identical starting phases”

Each component is and ODD integer multiple of the FFreq.

Question 12

Provide the first 4 components of a square wave starting at 200Hz:

Answer 12

200 x 1 = 200Hz

200 x 3 = 600Hz

200 x 5 = 1000Hz

200 x 7 = 1400Hz

Question 13

Provide first 4 components in sawtooth series with FF of 350Hz:

Answer 13

350 x 1 = 350Hz

350 x 2 = 700Hz

350 x 3 = 1050Hz

350 x 4 = 1400Hz

Question 14

The octave is:

Provide first 4 octaves with a f0 of 1000:

Answer 14

A doubling of frequency
A frequency ratio of 2:1 or 1:2

Ex.

200: 100 – 100:200
500: 250 – 250:500

1000Hz, 2000Hz, 4000Hz, 8000Hz

Question 17

Periodicity AKA:

Answer 17

Harmonics

Each line in an amplitude spectrum represents 1 frequency; the rest represent harmonics of the ff.

Question 18

Fundamental period/time:

What is it?

What’s it used for?

Answer 18

Ex: T = 8ms

Can use it to calculate a fundamental freq(125Hz)

But, cannot easily be used to determine all frequency components, amplitudes or starting phases.

Question 19

Sawtooth waves:

Answer 19

“Progressive summation of 3 components with identical starting phases”

Components are ODD & EVEN integer multiples

Question 20

Phase spectrum:

Answer 20

Defines starting phase as a function of frequency

Combination of amplitude spectrum and phase spectrum defines the waveform completely in the frequency domain

Question 21

Amplitude spectrum:

Answer 21

It shows amplitude as a function of frequency

X axis = amplitude
Y axis = frequency

Question 22

What does a waveform represent?

Answer 22

Represents the plotting of changes in some variable as a function of time.

Ex: displacement, velocity, acceleration, pressure etc. As a function of time.