うなり（トレモロ, tremolo)について

2003/3/12 Takuichi Hirano

うなり周波数の計算

In[1]:=

f1 = 880 ; f2 = 890 ; Print["•うなり周波数->２周波数の和 （積->和)"] ; Print["f1-f ... uot;] ; Print["(f1-f2)/2=", (f1 - f2)/2] ; Print["(f1+f2)/2=", (f1 + f2)/2] ;

•うなり周波数->２周波数の和 （積->和)

f1-f2= -10

f1+f2= 1770

•２周波数の和->うなり周波数 （和->積)

(f1-f2)/2= -5

(f1+f2)/2= 885

正弦波

In[9]:=

f = 880 ; ω = 2 * π * f ; dur = 2.0 ; wave[t_] := Sin[ω * t] ; Play[wave[t], {t, 0, dur}, SampleRate -> 44100, SampleDepth -> 16, PlayRange -> {-2, 2}]

[Graphics:HTMLFiles/index_9.gif]

Out[13]=

-Sound -

In[14]:=

Plot[wave[t], {t, 0, 3 * (2 * π)/ω}, PlotStyle -> {RGBColor[1, 0, 0]}, Ticks -> None, Frame -> True, FrameTicks -> None ]

[Graphics:HTMLFiles/index_12.gif]

Out[14]=

-Graphics -

２周波数の和

In[15]:=

f1 = 880 ; ω1 = 2 * π * f1 ; f2 = 890 ; ω2 = 2 * π * f2 ; dur = 2.0 ; wave ... y[wave[t], {t, 0, dur}, SampleRate -> 44100, SampleDepth -> 16, PlayRange -> {-2, 2}]

[Graphics:HTMLFiles/index_15.gif]

Out[21]=

-Sound -

In[22]:=

Plot[wave[t], {t, 0, 200 * (2 * π)/Min[ω1, ω2]}, PlotStyle -> {RGBColor[1, 0, 0]}, Ticks -> None, Frame -> True, FrameTicks -> None]

[Graphics:HTMLFiles/index_18.gif]

Out[22]=

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２周波数の積

In[23]:=

f1 = 885 ; ω1 = 2 * π * f1 ; f2 = -5 ; ω2 = 2 * π * f2 ; dur = 2.0 ; wave[ ... y[wave[t], {t, 0, dur}, SampleRate -> 44100, SampleDepth -> 16, PlayRange -> {-2, 2}]

[Graphics:HTMLFiles/index_21.gif]

Out[29]=

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In[30]:=

Plot[wave[t], {t, 0, 200 * (2 * π)/ω1}, PlotStyle -> {RGBColor[1, 0, 0]}, Ticks -> None, Frame -> True, FrameTicks -> None]

[Graphics:HTMLFiles/index_24.gif]

Out[30]=

-Graphics -

Converted by Mathematica  (March 12, 2003)