Can Arduino sound reproduce in microseconds at 1-4 kHz?

I just connected an electret microphone to the Arduino, and I would like to try between the 1 kHz and 4 kHz ranges .

I understand that this is limited to machine code and ADC , so I am trying to keep sketch simple.

Is it possible to sample between these frequencies using the sketch below?

const int analogPin = 0;
int ledPin = 13;

void setup() {
    pinMode(ledPin, OUTPUT);
}

void loop() {
    int mn = 1024;
    int mx = 0;
    for (int i = 0; i < 5; ++i) {
        int val = analogRead(analogPin);
        mn = min(mn, val);
        mx = max(mx, val);
    }
    if (mx-mn >= 50) {
        digitalWrite(ledPin, HIGH);
    }
    else {
        digitalWrite(ledPin, LOW);
    }
}