A tuning fork is sounded above a resonating tube (one end closed), which resonates at a length of 0.20 m and again at 0.60 m. If
the tube length were extended further, at what point will the tuning fork again create a resonance condition?
1 answer:
To solve this problem we will apply the concepts related to resonance. The velocity with which sound travels in any medium may be determined if the frequency and the wavelength are known. Since the pipe is closed at one end, that produces frequencies ratio 1:3:5, then
Third resonance occurs at
At resonance
Therefore at 1m will the tuning fork again create a resonance condition
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(1)
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The following relationship holds for an uniformly accelerated motion:
where S is the distance covered, vf the final velocity and vi the initial velocity.
If we take the moment the ball reaches the maximum height (let's call this height h), then at this point of the motion the vertical velocity is zero:
So we can rewrite the equation as
from which we can isolate h
Now let's assume that
Which is 4 times the height we found in (1). Therefore, the maximum height of ball 2 is 4 times the maximum height of ball 1.