The power-spectral density (PSD) of the thermal noise provides direct visualization of the contributions to the noise from each frequency. The PSD is proportional to the amount of power from voltage fluctuations at a given frequency, per unit frequency. The most prominent feature is a central plateau between the frequencies of the filters, with reduced spectral density at higher and lower frequencies. The flat plateau indicates white noise, while the roll-off at each edge comes from the filters. The entire spectrum is accurately described by combining a low pass-filter with a high-pass filter, so that the PSD (in decibels) is characterized by 4 A B S (dB) = 10 . log Here f is the spectral frequency, B the frequency of the high-pass filter, and C the frequency of the low-pass filter.The data listed below were obtained from measurements of thermal noise in a resistor (R=100 kOhms) at room temperature (7=295 K). The total gain was G=6.0x105. Fit these data to the expected theoretical function for the spectral density with high- pass and low-pass filters. The resulting high-pass filter frequency is _ Hz. f( Hz) S(dB) 20 -59.364 50 -45.348 100 -35.467 200 -32.913 500 -32.301 1000 -32.292 2000 -32.453 5000 -32.428 10000 -34.788 20000 -44.122 50000 -60.517 100000 -70.709Question 2 2 pts The amplitude of the white noise in a power spectral density can also be used to obtain Boltzmann's constant. Specifically, using the data from Quiz 3; Q1, find the average () for the 3 middle frequencies (500- 2000 Hz). Convert the decibels into a mean-squared voltage = 10/10. Treat this similar to other mean-squared voltages to obtain an experimental value for Boltzmann's constant, but note a few differences. The total gain is G=6.0x105 yielding = /G2, without the separate factor of 10, which is absent because the voltages were multiplied by the software, not the high-level electronics. The effective bandwidth is A f = 1 Hz because each point in the PSD spectrum is obtained by averaging the voltages over one second. The resulting dimensionless ratio between the experimental and accepted values of Boltzmann's constant is k(exp)/1.381x10-23 =