This is exactly what happens.
The sensitivity of the loudspeaker is 97.1 dB. When driven with the speech-shaped noise the SPL is 98.1 dB, an increase of 1.0 dB.
This results from the higher level of the speech-shaped signal in the frequency region where the loudspeaker has higher output capability compared to the rest of its pass band.
Conversely, if the low-frequency band-limited pink noise shown in Figure 4 were used to drive the loudspeaker it is reasonable to expect that the SPL would be less than when driven by the noise signal.
This results from the low-frequency pink noise signal having a higher level in the frequency region where the loudspeaker has lower output capability.
The SPL produced by the low-frequency pink noise is 94.9 dB, a decrease of 2.2 dB.
Figure 4: Spectral content of signal used to determine the sensitivity rating of loudspeaker A in Figure 1 (red) and of low frequency band limited pink noise (green). (click to enlarge)
Now let’s compare two different loudspeakers. Figure 5 shows loudspeaker A compared to loudspeaker B. Notice that they both have the same sensitivity, 97.1 dB.
Loudspeaker B, however, has greater low frequency and high frequency extension than loudspeaker A.
Figure 5: Magnitude response and single number sensitivity rating of loudspeaker system A (red) and loudspeaker B (black). (click to enlarge)
Because of this the bandwidth of the pink noise used to determine the sensitivity of loudspeaker B is greater than the bandwidth of the noise used for loudspeaker A (Figure 6).
As a result, the mid-band level of the noise for loudspeaker B is slightly less than that of the noise used for loudspeaker A. It’s a bit difficult to see but upon careful observation the black trace can be seen to be an average of 0.5 dB below the red trace from approximately 100 Hz-10 kHz.
Figure 6: Spectral content of signal used to determine the sensitivity rating of loudspeaker A (red), loudspeaker B (black), and broadband pink noise (green). (click to enlarge)
This is due to the greater bandwidth of the signal used for loudspeaker B (black trace). Remember that the broadband levels of both these signals are identical.
So what happens when each of these loudspeakers is driven by the broadband pink noise signal (20 Hz-20 kHz) also shown in Figure 6? As each of the loudspeakers used in this example are markedly not flat in their mid-band response there may be some tonal, and potentially measurably, differences in the SPL.
Hopefully, the reader can put these issues aside for the moment. All other things being equal, the loudspeaker with the greater effective frequency range (low- and high-frequency extension) should have greater SPL output.