The discussion focuses on calculating the frequency at which resonance occurs in a pipe when a piston is moved. The first resonance is at 0.045 m and the second at 0.151 m, with an initial frequency of 1620 Hz. The end correction is 0.008 m, leading to a calculated wavelength of 0.21 m. The final frequency for the third resonance is determined to be 1700 Hz, using the relationship between frequency, wavelength, and the speed of sound, which is assumed to be constant at 340 m/s.
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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?