A siren is producing a tone of frequency 10000 Hz, and a handheld decibel meter (like the one I use in class) is reading 20 dB. We've talked in class about how your perception of qualitative loudness (in phons) does not always match exactly with the meter. Using Fig 6.12 of your text to help, figure out, roughly, the "apparent loundness" (in phons) of this tone. (You may round to the nearest 5 phons. So if you think the answer is 6 phons, enter 5.)
To calculate the "apparent loudness" in phons, we need to use the concept of loudness level, which is measured in phons. Loudness level is defined as the sound pressure level (SPL) of a tone at a frequency of 1000 Hz, scaled by a set of equal-loudness contours.
In this case, we have a siren producing a tone at a frequency of 10,000 Hz, and a decibel meter registering 20 dB. We need to convert this measured sound pressure level at 10,000 Hz to the loudness level at 1000 Hz.
To do this, we can use Figure 6.12 from your textbook, which depicts equal-loudness contours. These contours represent the sound pressure levels at different frequencies that are perceived as equally loud to the human ear.
First, we need to locate the point on the x-axis of the graph that represents 10,000 Hz. Then, vertically above that point, we find the corresponding equal-loudness contour. The value on the y-axis of that contour is the loudness level at 1000 Hz that matches the perceived loudness of the siren at 10,000 Hz.
Based on your description, you've mentioned that the decibel meter is reading 20 dB. However, without additional information, it's unclear whether this reading corresponds to the sound pressure level at 10,000 Hz or if it's the overall sound level reading. To proceed, we will assume that the 20 dB reading corresponds to the sound pressure level at 10,000 Hz.
Let's assume that the 20 dB reading on the decibel meter represents the sound pressure level at 10,000 Hz. You can locate 10,000 Hz on the x-axis of Figure 6.12 and find the corresponding equal-loudness contour. The loudness level (in phons) at 1000 Hz is then determined by reading the value on the y-axis at that contour.
Please use your textbook's Figure 6.12 to determine the value on the y-axis (loudness level) of the corresponding equal-loudness contour for 10,000 Hz. Once you have that value, you can round it to the nearest 5 phons.