Question

You have a larger speaker of radius R and maximum excursion L. You now want to replace it with a speaker only 1/4 as large. What will the new excursion length have to be to be equally loud?

a) L/2
b) L
c) L/4
d) 2L

Answer 1

To maintain the same loudness when replacing a larger speaker with a smaller one that has a radius 1/4 as large, the new speaker's excursion needs to remain the same, which is option b) L.

Step-by-step explanation:

If you want to replace a larger speaker with a maximum excursion (how far the cone moves in one direction from rest) of L and radius R, with a speaker only 1/4 as large, you need to adjust the excursion accordingly to maintain the same loudness.

Loudness is generally related to the amount of air a speaker can move. Considering that the area of a speaker is proportional to the square of its radius, reducing the speaker's size by 1/4 implies the radius is halved (since the square root of 1/4 is 1/2).

To maintain the same loudness, the smaller speaker must move the same volume of air. Therefore, it would need to have the same excursion L, assuming its movement is linear and it's equally efficient. So the correct answer would be b) L.