Question

If a tuba is 20 dB louder than a singer’s voice, what is the ratio of intensities of the tuba to the voice?

Is this using Signal to Noise Ratio? I assumed Singal to Noise Ratio = 20 log (Vsignal / Vnoise) = 20 log (1/20) = -26.020  

Answer 1

As the given difference between two intensities is d = 20 dB. If we assume the intensity of tuba to be I1 and that of the singer to be I2 then the ratio of intensities of these two can be found using the difference between the two intensities.

Now, for each increase of 10 dB the intensity ratio gets increased by a factor of 10. In curren situation we have a difference of 20 dB which means that the there will be multiplication by square of 10 or 10 to the power 2, thus giving the ratio of intensities to be 100 . In simple words the tuba is 100 times louder than the singer.