Derive and sketch the frequency response of the loudspeaker of Example 18.13 for (1) k = 50,000 N/m and (2) k = 5 × 106 N/m. Describe qualitatively how the loudspeaker frequency response changes as the spring stiffness k increases and decreases. What will the frequency response be in the limit as k approaches zero? What kind of speaker would this condition correspond to?

Question

Example 18.13

A loudspeaker, shown in Figure 18.52, uses a permanent magnet and a moving coil to produce the vibrational motion that generates the pressure waves we perceive as sound. Vibration of the loudspeaker is caused by changes in the input current to a coil; the coil is, in turn, coupled to a magnetic structure that can produce time-varying forces on the speaker diaphragm. A simplified model for the mechanics of the speaker is also shown in Figure 18.52. The force exerted on the coil is also exerted on the mass of the speaker diaphragm, as shown in Figure 18.53, which depicts a free-body diagram of the forces acting on the loudspeaker diaphragm.

Answer 1

Analysis: