Maybe may I have this predict result ?
Your schematic of an LM386 power amplifier shows that you did not read its datasheet and did not read what I wrote in post #21:
1) Its maximum allowed input is only +-0.4V because it already has negative feedback for a voltage gain of 20. If you use an audio taper volume control at its input then when it is set to halfway your +-1.5V signal is reduced to +-0.15V and the amplifier output is +-3V.
2) It is already biased so the resistors you added to pin 3 are not wanted.
3) It must have a series RC at its output pin to ground as shown on EVERY circuit in its datasheet.
4) Your 100pF capacitor coupling its output to a speaker is for radio frequencies, not sound frequencies. Use 470uF.
5) Like ALL electronic circuits, its power supply pin needs a bypass capacitor to ground. Use 100uF to 470uF.
6) Its datasheet shows that with a 9V supply and driving an 8 ohm speaker its maximum output is +-3V, not +-4.5V.
But may I ask that why the input signal contain negative voltage but I do not need to add a negative voltage supply (they are connect to same ground)?
Is that LM386 has the internal dc coupling ?
It is designed for an input signal that swings positive and negative. It is designed to use only one positive supply voltage.
ALL modern amplifiers use internal DC coupling.