Question

What will be the difference in SIL of the sounds from two loudspeakers, one with an efficiency of 2.1% and one with an efficiency of 10.3%. Assume that all other variables, including the electrical power supplied, are the same in the two cases.

Answer 1

Since, the power supplied to the two speakers are same and only efficiencies are different, we can say that the intensity of sound produced will only different due to the efficiencies of the speakers.

,............EQ!

where, is the sound intensity produced

is the power supplied,

is the speaker efficiency

and is the proportionality constant

So, we can say that intensity of sound for speakers will be, (using EQ1)

,.........EQ2

where,

The sound intensity level (SIL in dB)is given by:

.............EQ3

where is the sound intensity level,

is the threshold of standard hearing

Thus the difference in the SIL for the two speakers will be, (Using EQ3)

............EQ4

Using EQ2, we get,

..............EQ5

substituting in EQ5, we get,