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For your final assignment this week, you will work out the following problems. Please show all your work. No credit will be given for incomplete answers.

- Using log
_{10}2 = .3, solve the following without using a calculator or log table. Please show your work!

- log
_{10}40 =

- log
_{10 }= - log
_{10}16 =

- The signal-to-noise ratio of a digital audio system can be derived from the following formula:

SNR_{dB} = 20 log 2^{n} *[n = number of bits per sample]*

- Simplify this expression to show that the signal-to-noise ratio can be expressed as 6n.

- Electrical power can be expressed in decibels using the following formula:

P_{dB} = 10 log_{10} *[P, P _{ref} = power (watts)]*

- If P
_{ref}= .001 watts, what is the power in dB when P = 1 watt?

- The output of an audio amplifier can be compared to its input using the following formula:

∆V_{dB} = 20 log_{10 } *[V _{out}, V_{in} = voltage (volts), ∆V = change in voltage]*

- Show that ∆V is always equal to 6 dB if the output is twice the voltage of the input.

- Using our decibel equations and a scientific calculator when necessary, solve the following. Please show your work!

- The input to an audio amplifier is known to be 2.5 watts, and the output is 25 watts. What is the gain of the amplifier in dB?
- The output of an amplifier is half the power of the input. Express the output in dB, relative to the input.
- How much voltage would appear at the output of a compressor indicating 7 dB gain reduction, if the input was 1.22 volts?
- An audio signal passes through two devices, each doubling its input voltage. What is the gain of the entire system, in dB?
- Two audio devices are placed in series such that:
- G
_{1}= 20 log ,*[G*_{1}= gain of device one] - G
_{2}= 20 log ,*[G*_{2}= gain of device two] - Show that
- G
_{3}= G_{1}+ G_{2},.*[G*_{3}= gain of device one and device two in series] - (
**Hint**: use the rule for expressing the log of a product as the sum of two logs.) - Post your decibels worksheet.