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!
- log1040 =
- log10 =
- 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]
- 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)]
- 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]
- 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:
- G1= 20 log , [G1= gain of device one]
- G2= 20 log , [G2= gain of device two]
- Show that
- G3= G1+ G2, [G3= 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.