Wave harmonics (calculate speed of wave)

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SUMMARY

The discussion focuses on calculating the speed of sound using a resonance experiment with a glass tube. A tuning fork with a frequency of 427 Hz was utilized, and resonance was observed at air column lengths of 17.4 cm and 55.0 cm. The calculated speed of sound was derived using the formula v = f x wavelength, leading to an approximate value of 321 m/s, which aligns with the book's answer. The end correction for the tube was also a point of inquiry, although not explicitly calculated in the discussion.

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  • Understanding of wave properties and harmonics
  • Familiarity with resonance in closed tubes
  • Knowledge of the speed of sound calculation
  • Proficiency in using the wavelength formula: wavelength = 4L/n
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Homework Statement


A glass tube with one end open and the other closed is used in a resonance experiment to determine the speed of sound. A tuning fork of frequency 427 Hz is used and resonance is observed for air column lengths equal to 17.4 cm and 55.0 cm.
(a) What speed of sound does this experiment give?
(b) What is the end correction for this tube?


Homework Equations


wavelength = 4L/n where n = 1,3,5,...
v = f x wavelength


The Attempt at a Solution


I assumed fundamental and second harmonics.
v = 427 x 4 x 0.174
v = 427 x 4/3 x 0.55
Although the answers don't exactly match, they're pretty close. However, the book answer is 321m s-1.

Could someone please help me arrive at the book answer or disprove it?
 
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