constexpr byte PIN_TO_SENSOR {3};
constexpr byte PIN_TO_BUZZER {9};
constexpr unsigned int RATE {500};
constexpr unsigned long FREQUENCY {1000000 / (RATE * 2)};

void setup() {
  Serial.begin(9600);
  pinMode(PIN_TO_SENSOR, INPUT);
  pinMode(PIN_TO_BUZZER, OUTPUT);
  Serial.println (FREQUENCY);
}

void loop() {
  static bool isBuzzerOn {false};
  static byte pinStatePrevious {LOW};

  byte pinStateCurrent = digitalRead(PIN_TO_SENSOR);
  if (HIGH == pinStateCurrent && false == isBuzzerOn) {
    tone(PIN_TO_BUZZER, FREQUENCY);
    isBuzzerOn = true;
    Serial.println("Motion detected");
  } else if (LOW == pinStateCurrent && true == isBuzzerOn) {
    noTone(PIN_TO_BUZZER);
    isBuzzerOn = false;
  }
}
Click on the PIR sensor to trigger a motion detection.