Batteries in parallel vs voltage signals in parallel
Output is always the weighted average (superposition) of inputs.

Consider the following circuit in which two voltage sources are connected to the same load. 







simulate this circuit &ndash; Schematic created using CircuitLab

Let V1 and V2 be DC sources then by superposition theorem,
$$V_O = (V_1 + V_2)/3 \tag{1}$$

Assumed that  R1,R2 = RL.

If V1 and V2 be monotonic ac signal sources then we can write, \$V1 = A_1 \cos (2\pi f_1 t)\$ and \$V2=A_2\cos (2\pi f_2 t)\$. Then, 

case1: \$f_1 = f_2 = f\$ then,
$$V_O = \frac{(A_1+A_2)}{3}\cos(2 \pi f t)\tag2$$

Here both sources generates same tone when connected to a speaker (load). Then output is same tone with output amplitude =  superposition (weighted average) of the two input signals. 

case2: \$f_1 \ne f_2 \$ then,
$$V_O = \frac{A_1 cos(2 \pi f_1 t) +A_2 cos(2 \pi f_2 t)}{3} \tag3$$

Here both sources generates different tone when connected to a speaker (load). When both connected together, output signal will have both the tones (\$f_1\$ and \$f_2\$) as given by expression (3). Hence both the tones can be heard at the output. 

If V1 and V2 are audio signals then they will have lot of frequency components in it (given by the Fourier transform). When connected to same speaker, output will also contain all these frequencies and hence one can hear both the audio signals.