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A child swinging on a swing set hears the sound of a whistle that is being blown directly in front

of her. At the bottom of her swing when she is moving toward the whistle, she hears the higher
pitch, and at the bottom of her swing, when she is moving away from the swing she hears a lower
pitch. The higher pitch has a frequency that is 5.0% higher than the lower pitch. What is the
speed of the child at the bottom of the swing?

I think I need to use the equation
freq observed=[(1-v child)/v sound]freq sound

I know the v sound =343 m/s but I have no idea even where to start on this question.

2 answers

okay, so I set it up as a ratio:
[(1-v child)/v]*freq sound
OVER
[(1+v child)/v]*freq sound
ALL THAT =1.05

So I have 1.05=[(1-v child)/343]/[(1+v child)/343]

But I can't figure out how to manipulate this equation. I keep getting the v child as 341 m/s, and I know that kid is not moving that fast! How do I finish this equation?
I guess I gave up too soon!