How Does Doppler Effect Influence Perceived Sound Frequency?

[frozen7]

7. A block with a speaker bolted to it is connected to a spring having spring constant k = 20.0 N/m as in Figure 3. The total mass of the block and speaker is 5.00 kg, and the amplitude of this unit’s motion is 0.500 m. If the speaker emits sound waves of frequency 440 Hz, determine the range in frequencies heard by the person to the right of the speaker.
Ans: [ 439 Hz < f < 441 Hz ]


Can anyone help me to solve this? Give me some clues please.

 

[frozen7]

I do it in this way:

1/2 k x^2 = ma
a = 0.5
And I found the value of v1 (speed of speaker) = 0.707 by using v1^2 = u^2 =2as

Then I find the max frequency by f`=f ( v / ( v-v1))
min frequescy = f`=f ( v / ( v+v1))


Am I doing correctly?