# Ans Doc 32

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 log102 = .3, solve the following without using a calculator or log table. Please show your work!
1. log1040 =
1. log10 =
2. log1016 =
• The signal-to-noise ratio of a digital audio system can be derived from the following formula:

SNRdB = 20 log 2n [n = number of bits per sample]

1. 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:

PdB = 10 log10  [P, Pref = power (watts)]

1. If Pref= .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:

∆VdB = 20 log10  [Vout, Vin = voltage (volts), ∆V = change in voltage]

1. 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!
1. 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?
2. The output of an amplifier is half the power of the input. Express the output in dB, relative to the input.
3. How much voltage would appear at the output of a compressor indicating 7 dB gain reduction, if the input was 1.22 volts?
4. An audio signal passes through two devices, each doubling its input voltage. What is the gain of the entire system, in dB?
5. Two audio devices are placed in series such that:
6. G1= 20 log  , [G1= gain of device one]
7. G2= 20 log  , [G2= gain of device two]
8. Show that
9. G3= G1+ G2[G3= gain of device one and device two in series].
10. (Hint: use the rule for expressing the log of a product as the sum of two logs.)