That is a bit on the high side, but not wildly so. You can only hear 20K Hz max and most speakers roll off around 10KHz to 15Khz, unless you are talking HiFi speakers. In case you are interested there is a breed of class D chips that are called 'filterless' that for economy rely on the inductance/resistance and frequency response of the speaker and leads to effectively filter the class D switching signal.
I did get the scope reading . Although the signal may seem high, have no fear, it will not damage your speakers- you want to see the switching signal on our TV and and my laptop.
The 370kHz at a level of 0.3V RMS produces a whopping high power of 0.01W in an 8 ohm resistor but since most speakers are inductive then the power in a speaker is much less. Nothing to be worried about.