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

f1 = 880;
f2 = 890;
Print["■\:3046\:306a\:308a\:5468\:6ce2\:6570->\
\:ff12\:5468\:6ce2\:6570\:306e\:548c \:ff08\:7a4d->\:548c)"];
Print["f1-f2=", f1 - f2];
Print["f1+f2=", f1 + f2];
Print["■\:ff12\:5468\:6ce2\:6570\:306e\:548c->\
\:3046\:306a\:308a\:5468\:6ce2\:6570 \:ff08\:548c->\:7a4d)"];
Print["(f1-f2)/2=", (f1 - f2)/
          2];
Print["(f1+f2)/2=", (f1 + f2)/2];

正弦波

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}]

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

２周波数の和

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

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

２周波数の積

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

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