sine wave that slowly ramps up frequency from f1 to f2 for a given time

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if you want angular frequency (w=2 pi f) to vary linearly with time then dw/dt = a and w = w0 + (wn-w0)*t/tn (where t goes from 0 to tn, w goes from w0 to wn). phase is the integral of that, so phase = w0 t + (wn-w0)*t^2/(2tn) (as oli says):

void sweep(double f_start, double f_end, double interval, int n_steps) {
    for (int i = 0; i < n_steps; ++i) {
        double delta = i / (float)n_steps;
        double t = interval * delta;
        double phase = 2 * PI * t * (f_start + (f_end - f_start) * delta / 2);
        while (phase > 2 * PI) phase -= 2 * PI; // optional
        printf("%f %f %f", t, phase * 180 / PI, 3 * sin(phase));
    }
}

(where interval is tn and delta is t/tn).

here’s the output for the equivalent python code (1-10Hz over 5 seconds):

1-10 Hz over 5 seconds

from math import pi, sin

def sweep(f_start, f_end, interval, n_steps):
    for i in range(n_steps):
        delta = i / float(n_steps)
        t = interval * delta
        phase = 2 * pi * t * (f_start + (f_end - f_start) * delta / 2)
        print t, phase * 180 / pi, 3 * sin(phase)

sweep(1, 10, 5, 1000)

ps incidentally, if you’re listening to this (or looking at it – anything that involves human perception) i suspect you don’t want a linear increase, but an exponential one. but that’s a different question…

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