In the experiment, a meter is hooked up to a speaker to monitor the amplitude of the received sound. Suppose the background signal level is 15 mV, the signal is 90 mV with no attenuator and is 30 mV with an attenuator in place. Calculate pt/pi including the background correction.
To calculate pt/pi, which represents the transmission coefficient of the attenuator, we need to consider the background correction. The background correction takes into account the background signal level and adjusts the difference between the signal level with and without the attenuator.
Let's break down the calculation step by step:
1. Calculate the background-corrected signal without the attenuator:
pt = signal level without attenuator - background signal level
= 90 mV - 15 mV
= 75 mV
2. Calculate the background-corrected signal with the attenuator:
pi = signal level with attenuator - background signal level
= 30 mV - 15 mV
= 15 mV
3. Calculate pt/pi (transmission coefficient):
pt/pi = pt / pi
= 75 mV / 15 mV
= 5
So, the value of pt/pi, including the background correction, is 5.
Note: The unit for pt/pi is mV/mV, and it represents the ratio of the transmitted signal amplitude without the attenuator (pt) to the transmitted signal amplitude with the attenuator (pi).