A Block, a speaker and a spring

[Trista]

I love it when they combine chapters. :rofl:
OK, here is the question:
A Block witha speaker bolted to it is connected to a spring having spring constant k = 20.0 N/m. the total mass of the block and speaker is 5.0 kgk, and the amplitude of the unit's motion is 0.500 m. If the speaker emits sound waves of frequency 440 Hz, determine the lowest and highest frequencies heard by the person to the right of the speaker.


Lets see if I can draw this in ASCII. The periods are for spacing purposes.

|
|
|
|......... Me standing to the
|...|---/\ ) ) ) .........right of the speaker
|...|---\/ ) ) ).<-- (speaker and sound waves).trying to decide the
|()()|.<-(spring attached to the block and sp)... lowest and highest
|............ frequencies.
|

Ok, so the spring constant part has thrown me. I'm not sure where to begin. Can someone help?

 

[Chi Meson]

How does the spring constant relate to maximum potential energy? And how does this relate to maximum kinetic energy? And how does kinetic energy relate to its fastest speed? And how does speed relate to shift in perceived frequency?

 

[Trista]

ok, one thing at a time...
PE spring = KE
1/2kA^2 = 1/2mv^2 max so,
1/2(20 N/m)(0.50 m)^2 = 1/2 (5.0 kg) v^2 max
2.5 = 1/2 (5.0 kg) v^2 max
v max = sq rt [2(2.5 m)/5 kg]
v max = 1 m/s

if that is right then,
now I need to deal with perceived frequency.

 

[Chi Meson]

Hello? Mr. Doppler?