Question: Can the rms AC voltage change with frequency?

I have connected a DSO to the audio oscillator(having 10V p-p). Peak to peak voltage remains constant on changing frequency(10 Hz to 100KHz) but on measuring the rms voltage with a multimeter, the voltage varies drastically(falls off from 3.4V at 500Hz to 0.5V at 50KHz).

Is something wrong with the oscillator/multimeter? **Can AC rms voltage vary even when peak to peak value remains constant?**

Answer: 
Most multimeters aren't designed for the frequencies you are using. They are generally intended to be used at around line frequency (50hz or 60Hz.) Some will also work at higher frequencies, some won't. Around 10Hz you aren't too far from what the meter expects, so it works OK. At higher frequencies, it won't work so good.

The multimeter will have filters on its input that limit the frequency range of the input signal. Check the specifications of your meter to see what range it is guaranteed to work in. You may find that it is only specified for, say, under 200Hz or maybe just at 60Hz or just at 50Hz.

[Here is a good multimeter,](http://rads.stackoverflow.com/amzn/click/B002X9IPB2) and it only goes upto 30kHz.

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In response to comment:

[Your Fluke 115](http://en-us.fluke.com/products/digital-multimeters/fluke-115-digital-multimeter.html#techspecs) is only specified for up to 1kHz when measuring AC RMS voltage. Above that, anything goes. So, your meter is misleading you.
If the measured signal is a pure sinusoid then RMS should remain the same.
So chances are:

* the multimeter is not measuring the real RMS
* the shape of the output changes ( maybe more noise or higher frequency harmonics )