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## Homework Statement

The coil in a loudspeaker has an inductance of L = 56uH (or 5.6 x 10^-5 H). To produce a sound frequency of 20 kHz, the current must oscillate between peak values of +2.2 A and -2.2 A in one half of a period. What average back emf is induced in the coil during this variation? How does this compare to the applied emf of 18V?

## Homework Equations

T = 1/f

emf = L(ΔI/Δt)

L = N(ΔΦB/Δl)

## The Attempt at a Solution

back emf = (5.6 x 10^-5)[+2.2 - (-2.2)/Δt]

My problem here is I do not know where I can obtain Δt. I am assuming that it has something to do with the frequency of 20kHz in one half period (1/2T).

T = 1/f --> 1/2T = 1/f --> 2/f -- > T = 2/20000 = 1.0 x 10^-4 secs

If this is the case then, by subbing, Δt = 1.0 x 10^-4 secs, into the above equation, I get:

back emf = (5.6 x 10^-5)[+2.2 - (-2.2)/1.0 x 10^-4 secs]

= (5.6 x 10^-5)[4.4/1.0 x 10^-4 secs]

= (5.6 x 10^-5)(44000)

= 2.464 V

Is this correct?