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.
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To calculate pt/pi including the background correction, we need to consider the signal level with and without the attenuator in place, as well as the background signal level.
The equation for calculating the power transmitted (pt) with the attenuator is:
pt = pi × (V / V0)²
Where:
- pt is the power transmitted
- pi is the input power without the attenuator
- V is the signal level with the attenuator
- V0 is the background signal level
Given:
- The background signal level (V0) is 15 mV
- The signal level without the attenuator (V) is 90 mV
- The signal level with the attenuator (V) is 30 mV
First, let's calculate the input power without the attenuator (pi) by rearranging the formula:
pi = pt / (V / V0)²
Substituting the values:
pi = pt / (90 / 15)²
pi = pt / 6²
pi = pt / 36
Now, let's calculate the power transmitted (pt) with the attenuator by rearranging the formula:
pt = pi × (V / V0)²
Substituting the values:
pt = (pt / 36) × (30 / 15)²
pt = (pt / 36) × 2²
pt = (pt / 36) × 4
pt = (pt × 4) / 36
Finally, let's include the background correction by calculating pt/pi:
pt/pi = [(pt × 4) / 36] / (pt / 36)
pt/pi = (pt × 4) / pt
pt/pi = 4
Therefore, pt/pi including the background correction is 4.