The lousy old LM358 is low power so it is slow. It can barely have a gain of 10 at 40kHz then its output is triangle-waves instead of square-waves.

Thanks Audioguru
Can you suggest a replacement for my "lousy old LM358".

 

The lousy old LM358 dual opamp has hardly any gain and output above 5kHz.
An MC34072 dual opamp works fine with a 5V supply and with frequencies up to 100kHz.

 

Just as a suggestion, what if you place a short across the receiver temporarily. If you continue to see a signal on the oscope, then you have to conclude that at least some of the output is electrical noise rather than acoustical in origin.

hgmjr

Thanks for your suggestion, I blocked the receiver with my thumb - no signal. I blocked the transmitter with my thumb - no signal. I shorted across the receiver – no signal. I disconnected the receiver - no signal.

Conclusion the problem is acoustic crosstalk.