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It depends on what frequency you're generating. If the pulse width is longer than the RC time constant, then the output will be an exponentially decaying pulse.
The RC time constant is your 220uf capacitor and the resistance or impedance of the load.
If the load resistance is low or if the frequency is low then the square-wave will be differentiated into spikes.
Before you wanted a square-wave. Now you want a 960Hz sine-wave?
A 960Hz square-wave also has the odd-numbered harmonics at 2880Hz, 4800Hz, 6720Hz, 8640Hz, 10560Hz, 12480Hz, 14400Hz, 16320hz, 18240Hz and 20160Hz. The output of a 555 oscillator is almost a square-wave. It is actually a rectangular-wave with some even-numbered harmonics added in. You can make a 555 produce a square-wave if you connect it as an inverting Schmitt trigger.
The 555 will overheat when it tries to drive an 8 ohm speaker. You must add a resistor in series with the speaker to limit the current to no more than 200mA but then the speaker will not be loud.
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