Answer to Question #276219 in Physics for Kaidi

Question

1. Determine the driving force constant b of a spring whose spring constant is 241N/m and has a 0.454kg mass connected to its free end if its period of oscillation is 0.287s.
2. A certain stopped pipe has a fundamental frequency of 187.3Hz. The second overtone of this pipe has the same wavelength as the third harmonic of an open pipe. How long are the two pipes? Assume that the speed of sound in the pipes is 340 m/s.

Answer 1

1)

$$\frac{1}{0.287}=\frac{1}{2\pi}\sqrt{\frac{241}{0.454}-\frac{b^2}{4(0.454)^2}}\\b=6.52\frac{Ns}{m}$$

2)

$$5(187.3)=\frac{3(340)}{4L}\\L=0.273\ m$$