The discussion revolves around the resonance frequencies of sound waves in a pipe with a speaker and a piston. The original poster presents a scenario involving two resonance points and seeks to determine the frequency at which resonance occurs again after increasing the frequency slightly. Key parameters include the end correction, wavelength, and speed of sound.
The conversation is ongoing, with participants sharing calculations and questioning the accuracy of their results. Some have provided insights into the relationships between frequency and wavelength, while others are clarifying the conditions under which resonance occurs. There is no explicit consensus yet on the correct frequency for the third resonance.
Participants note discrepancies in calculated values and the original problem statement, leading to discussions about potential errors and assumptions in their calculations. The end correction and its impact on wavelength are also under consideration.
Here is what I think happened. Whoever made the answer key thought ##L_3(λ') = \frac 4 5 λ'-ε##. That would give 1710hz for the frequency. Rounding to 2 significant digits, it would be 1700hz.Helly123 said:Maybe
##L_3(\lambda')## = ##\frac{5}{4}\lambda## - ε
0.151 = ##\frac{5}{4}\lambda## - 0.008
##\frac{5}{4}\lambda## = 0.159
##\lambda## = 0.2 * 4/5 = 0.16 = 0.2 m
That way, frequency = 340/0.2 = 1700 Hz
How can you assume the 1710 Hz? How to get that result?tnich said:Here is what I think happened. Whoever made the answer key thought ##L_3(λ') = \frac 4 5 λ'-ε##. That would give 1710hz for the frequency. Rounding to 2 significant digits, it would be 1700hz.
Using ##\frac 4 5 λ## instead of ##\frac 5 4 λ##, but that would not be correct.Helly123 said:How can you assume the 1710 Hz? How to get that result?