# The minimal signal to noise ratio (SNR) for people to understand a speech in the noisy background

This question seems easy to find an answer but I got lost in the end. I am trying to find the threshold for people to understand speech in a noisy environment. For example, assume the background noise is $\mathbf n$ and the speech signal is $\mathbf s$. I wanna know the threshold thr for the speech being recognizable by a human when: $$10\log\left(\frac{\lVert \mathbf s\rVert}{\lVert \mathbf n\rVert}\right) > \text{threshold}\implies\quad\text{so the speech \mathbf s is recognizable by human}$$

The most relevant scientific fact I found is the absolute hearing threshold, such as the ISO 226.

However, I got confused to interpret this ISO 226 figure because the $y$-axis is in SPL (dB). Based on my understanding, the SPL is also defined based on the minimal hearing threshold, which is kind of weird to understand how much signal strength (of a speech) is actually necessary for people to recognize.

• Can I say the signal strength of a $10\textrm{ kHz}$ signal needs to be $\approx 5\textrm{ dB}$ higher than the noise floor for being recognized by the human based on the red lines shown in this ISO 226 figure?
• If it is true, how can I know the threshold for a speech signal covering multiple frequencies?
• SNR is defined as $10 \log_{10} \left(\frac{ \| \mathbf{s} \|^2}{\| \mathbf{n} \|^2} \right)$. Feb 8 at 12:50
• I took a speech signal in Audacity and added an overlapping channel with white noise. When the SNR (measured by Audacity's contrast) was about 1 dB I could hear the speech relatively well. When the SNR was -10 dB I couldn't hear the speech. Feb 8 at 12:51