The $50-from-China-via-ebay NJM4556-based headphone amp, pictured below, fails the "Is thing thing on?" test. With 16 ohm, 104 dB/mW headphones there is a faint-yet-audible background hiss when the unit is powered up and the volume is turned all the way down. The hiss increases only slightly as the volume is turned up (input disconnected).

The output noise of an op amp is normally estimated from the input-referred voltage noise density multiplied by the gain, and the current noise density multiplied by the gain and the sum of the input impedances on the inverting and noninverting inputs. The NJM4556 datasheet does not give a figure for current noise, but a reasonable guess is 1 pA/sqrtHz. The voltage noise density is estimated at 8 nV/sqrtHz.

Total noise is

Vn (output) = sqrt [(i_n R_s)^2 + e_n^2 + 4kT R_s] * Gain

Working from a source impedance of ~10k, I get about 18 nV/sqrtHz or -138 dB.

[Revised according...