Calculate the amplitude change in decibels given an initial amplitude of 1,000 Volts and a final amplitude of 10 Volts.

Question

A. -10 dB

B. -20 dB

C. -30 dB

D. -40 dB

Answer 1

One decibel is 20 times the log of the voltage ratio. Suppose 2 voltages are related by a factor of 10. The log of 10 is one, and so a factor of 10 is 20dB.

In the stated problem, the change in voltage is 100 times The log of 100 is 2, so the change in dB is 2 * 20 = 40dB

Answer 2

Decibels use a base-10 logarithmic system, meaning 10 decibels increases the magnitude by 10 times.

+10 dB = 10,000 Volts

0 dB = 1000 Volts (starting point)

-10 dB = 100 Volts (1000/10 = 100)

-20 dB = 10 Volts (ending point) (100/10 = 10)

-30 dB = 1 Volt

The Answer is B) -20 dB