Motion of point when sound volume goes up

[JessicaHelena]

Homework Statement

A radio speaker produces sound when a membrane called a diaphragm vibrates, as shown above. A person turns up the volume on the radio. Which of the following aspects of the motion of a point on the diaphragm must increase?

a) the max. displacement only
b) the average speed only
c) both a) and b)
d) neither a) nor b)

(This is an AP Physics 1 sample problem)

Homework Equations

v=f * lambda (?)

The Attempt at a Solution

I know that the displacement will increase bc a louder volume leads to a greater amplitude (which is the displacement). The answer says that the average speed too must increase (it is choice c), but I'm having a hard time understanding that: I thought that loudness — and so amplitude — has nothing to do with the speed.

 

[mfb]

The frequency stays the same. How would you travel a larger distance in the same time without increasing the speed?

This is not the speed of the wave propagation (which stays constant). It is the speed of the membrane - much slower than the speed of sound.