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Well kind of a capacitor can only do so much in this situation. They are good at smoothing the waveform of AC, BUT a capacitor will always allow some ac fluctuations to the device. As ac-dc suggested putting in another capacitor would not solve the problem. You could add a band stop filter to the speaker itself, which would use a capacitor... but the simple solution is to use another voltage regulator, a three pronged chip, to control the voltage. Additionally this would help with the current voltage drift under load. If you have any further questions feel free to ask i love to help clear up things and help others to learn.
Oh sorry to be misleading... Yes you could calculate the if you had the right capacitor, but this is where we begin exceeding my knowledge of capacitor theory. I wish you luck over the matter, and I am glad to have learned something today.
Yes that is understood, BUT the DC source here is from a wall wart(assumed). They work by using a transformer to step down the ac from your house 110Vac to the required voltage, eg. 1.5Vac it is then rectified by a diode array. turning it into a bumpy one-sided DC wave. The DC is then passed into a capacitor that "filters" it smoothing the wave form, producing DC. There is still a saw wave on top that acts like a AC wave, that "wave" is oscillating at 60Hz giving the annoying hum. For more information click here.
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