Question

Question: (I) A 5000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.)

Short answer

The \(5000{\rm{ Hz}}\) tone should have a \(20{\rm{ dB}}\) sound level to get loudness, same as the tone with frequency \(100{\rm{ Hz}}\) and sound level \(50{\rm{ dB}}\).

Step-by-step solution

Step-1:-Loudness of the sound

In the graph, each curve represents the equally loud sounds for different frequencies in Hertz at different sound levels in Decibels.

Step-2:-Given data

The sound level of tone with frequency \(100{\rm{ Hz}}\) is \(50{\rm{ dB}}\).

The frequency of the tone for which the sound level is to be found is \(5000{\rm{ Hz}}\).

Step-3:-Calculation of sound level

The following is the graph between sound level, frequency and intensity.

As seen in the graph, the loudness is \(20{\rm{ phons}}\) for the tone with frequency \(100{\rm{ Hz}}\) and the sound level \(50{\rm{ dB}}\). On the other hand, for the \(5000{\rm{ Hz}}\) tone, the \(20{\rm{ phons}}\) loudness is at the sound level of \(20{\rm{ dB}}\).