What Is the Correct Water Level for the Third Resonance in a Closed-Open Tube?

AI Thread Summary
The discussion focuses on determining the correct water level for the third resonance in a closed-open tube when using a tuning fork with a frequency of 512 Hz. The speed of sound is given as 343 m/s, and the resonance levels are calculated using the formula for a closed-open tube. Initial calculations suggest that the third resonance corresponds to a water level of 50.2 cm, but this is disputed as it misinterprets the value of n. The correct approach involves recognizing that n does not directly correlate to the resonance number, and understanding the positions of nodes and antinodes is crucial for accurately identifying resonance levels. Ultimately, the correct water level for the third resonance is identified as 83.7 cm.
Any Help
Messages
79
Reaction score
2

Homework Statement



A vibrating tuning fork of frequency 512 Hz is held over a water column with one end closed and the other open. As the water level is allowed to fall, a loud sound (resonance) is heard at specific water levels. Assume you start with the tube full of water, and begin steadily lowering the water level. What is the water level (as measured from the top of the tube) for the third such resonance? Take the speed of sound in air to be 343 m/s.


  • A

    83.7 cm


  • B

    16.7 cm

  • C

    33.5 cm
  • wrong-icon.png


    D

    50.2 cm


  • E

    167 cm

Homework Equations



in a fundamental frequency (f):
λ=2L/n and f=n/2L .v for waves whose both ends are open
λ=4L/n and f=n/4L .v for waves whose one end closed and the second is open
n is a positive integer; n= 0,1,2,3,4,5,6...
v is the velocity
L is the length of string
λ is the wavelength

The Attempt at a Solution


here we have one open and other closed ends then we use λ=4L/n and f=n/4L .v
so f=512Hz, n=3 (third such resonance) and v=343m/sec
substitute in the equation
we get L equal 0.502m=50.2cm then it is D
but why the correct answer is A??
 
Last edited by a moderator:
Physics news on Phys.org
n = 3 is incorrect. The best thing to do for these types of problems is to draw a diagram of the standing wave for the situation. You can then determine L from the diagram.
 
Last edited:
TSny said:
n = 3 is incorrect. The best thing to for these types of problems is to draw a diagram of the standing wave for the situation. You can then determine L from the diagram.
I didn't get your point. How can I draw diagram for it? Besides why n=3 is not correct? what do they mean by the third such resonance?
 
Any Help said:
How can I draw diagram for it?
When the level of the water is at a position of resonance, what can you say about the positions of nodes and antinodes, especially at the top of the tube and at the top of the water? You can use this knowledge as a guide for drawing the various cases where you get resonance.
Besides why n=3 is not correct?
The n in the formula does not necessarily correspond to the number of the resonance. Thus n = 3 does not correspond to the third resonance in your situation.
What do they mean by the third such resonance?
Imagine the water level starts at the top of the tube. As the level of the water is lowered in the tube while the fork is vibrating, there will be certain positions of the level of the water that will cause the sound from the fork to resonate. The first level that produces a resonance is the first resonance. The next level of water that produces resonance is the second resonance. And so on.
 
Last edited:
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

Similar threads

Back
Top