Start by trying to read the PIR sensor and make the onboard LED switch on when the sensor is triggered.
Will do. Then after that what's next?
Attempt to generate this signal, depending on the transducer type. Maybe the tone() function works for this.
What is the best transducer for homebase that will generate 15KHz-29KHz?
You can make it quite easily and then buy an amplifier and a HIFI tweeter that will reproduce those sounds.
Make an audio frequency oscillator to cover the range you want. There must be lots of circuits if you Google audio oscillator.
You can us e the Arduino to turn the oscillator on and off. OR leave it on all the time and turn the amplifier on and off.
You will need a proper power supply for the amplifier.