To answer your question, if this is the same or similar to Popular Electronics circuit I mentioned earlier, the output speaker sets up an ultrasonic field, which the input speaker and circuit receives. Note the two diodes in front of the op amp, this is a AM detector. If something moves in this U/S field the U/S frequency is dopplered, which means frequencies slightly above and below the U/S carrier are formed, which means the diodes will have a very low frequency (around 1Hz, give or take, depending on the speed the object is moving) feed into the op amp. This will in turn trigger the relay activating an alarm.

In other words, it is a simple motion sensor.

No it is not a motion sensor.
The rectified ultrasonic signal is filtered to produce DC which is amplified to turn on the relay when ultrasonics is received.

A motion detector uses a second AM detector diode to demodulate the additions and cancellations of a reflected ultrasonic beam that is modulated by motion.

Here is an ultrasonic motion detector project:

 

I see one AM detector in the OPs design, what do you think the relay is for? If it were a simple detector of U/S, there would have to be filtering.

 

I see one AM detector in the OPs design, what do you think the relay is for? If it were a simple detector of U/S, there would have to be filtering.

Piezo transducers have a fairly high Q bandpass response, and so provide their own filtering, providing that a matching transducer is used in the transmitter.

 

The circuit posted by the OP simply turns on the relay whenever ultrasonics is present because it rectifies the received carrier (but it was not designed properly so the relay is turned on all the time).
A motion detector ignors the carrier and rectifies the modulation caused by motion so it can turn on a DC alarm.

 

The OP design is a tweeter, not a piezo. The only other alternative is it is simple go/no go U/S receiver from what I can see. There is a high gain amplifier with no AC coupling feeding into a FET input op amp. This can be triggered by almost any sound the speaker can pick up. Strange.

 

also tell that how can i identify the terminals of u.sonic transducer.one terminal is shorted to metal surface of transducer is this a gnd?

I interpreted this description to mean he is using piezo transducers.
EDIT: Perhaps a more definitive term for what I envisioned is ultrasonic transducer.

 

This can be triggered by almost any sound the speaker can pick up. Strange.

It also picks up hand claps and glass breaking.