Why does an oscilloscope show a different voltage from a signal generator?

The DG1022 signal generator has an output impedance setting- High Z and 50\$\Omega\$ (or some other resistance).

If you set it for 50\$\Omega\$ then you need to terminate it with 50\$\Omega\$ or you'll get double the output voltage!

Set it to High Z and all will likely be well.

Generally the voltage setting on generators is half of what the open circuit output voltage is, though it depends on the generator. Usually signal generators are designed to drive a 50 ohm load, so they have a 50 ohm source impedance for matching purposes. As a result, the voltage across the load will be proportional to the load impedance. If the generator puts out 1 volt at no load, then you will get 0.5V across a 50 ohm load (the 50 ohm source and load impedances act like a voltage divider). The output voltage setting compensates for this. Try setting your scope input to 50 ohms, if it supports this. If not, connect them both to a 50 ohm resistor. It may also be possible to disable the 50 ohm load impedance compensation in the generator.

By the way, the peak-to-peak voltage will be about 2.8 times the RMS voltage, so 3.276 x 2.8 = 10.276. So the scope is showing the correct voltage, it's just not the voltage you were expecting.

The proper way to calibrate the probe and scope is with a square wave as provided in the lower right corner.

This way frequency response and DC gain are both checked.

To calibrate probes, read manual for auto-compensation. To calibrate gain, read the autocal section of manual.

Disconnect any probes or cables from all channel inputs, otherwise failure or damage to the oscilloscope may occur. Press →Self-Cal to enter the self-calibration interface as follows. Press “RUN/STOP” key to start the operation and press “AUTO” key to exit the system

If the generator gives the same result with a 50 Ohm load, consult factory.

With high impedance load, expect result to be 2x selected output. Output drops 50% with a matched load.