Analyze Wave Amplitude and Energy Practice Test

A student shakes a rope to send a traveling wave. Keeping the frequency the same, they want the wave to carry 9 times as much energy as before. For waves on a rope, $E \propto A^2$. What must happen to the amplitude?

A loudspeaker produces a sound wave at a fixed frequency. When the volume knob is turned up, the sound wave’s amplitude increases from $A_1$ to $2A_1$ while the listener stays at the same distance. If sound intensity (and energy transfer rate) is proportional to amplitude squared, $I \propto A^2$, by what factor does the sound intensity change?