A student is using a resonance tube and determines that three resonances occur at distances of L1 = 0.513 m, L2 = 0.855 m, and L3 = 1.212 m below the open end of the tube. The frequency of the tuning fork used is 4.80 102 Hz. (Enter your answers to at least three significant figures.) HINT (a) Find the wavelength (in m) using distances L2 and L1. λ2-1 = 984.96 Incorrect: Your answer is incorrect. m (b) Find the wavelength (in m) using distances L3 and L2. λ3-2 = m (c) Find the average wavelength (in m). λavg = m (d) Find the average speed of sound (in m/s).

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boffeemadrid boffeemadrid · Answer 1 · 2019-12-09T09:10:13+01:00

Answer:

0.685 m

0.714 m

0.699 m

336 m/s

Explanation:

[tex]L_1=\frac{\lambda}{4}\\\Rightarrow \frac{\lambda}{4}=0.513[/tex]

[tex]L_2=\frac{3\lambda}{4}\\\Rightarrow \frac{3\lambda}{4}=0.855[/tex]

[tex]L_3=\frac{5\lambda}{4}\\\Rightarrow \frac{5\lambda}{4}=1.212[/tex]

[tex]L_2-L_1=\frac{\lambda}{2}=0.855-0.513\\\Rightarrow \lambda=2\times 0.342\\\Rightarrow \lambda=0.685\ m[/tex]

[tex]\lambda=0.685\ m[/tex]

[tex]L_3-L_2=\frac{\lambda}{2}=1.212-0.855\\\Rightarrow \lambda=2\times 0.357\\\Rightarrow \lambda=0.714\ m[/tex]

[tex]\lambda=0.714\ m[/tex]

[tex]L_3-L_1=\lambda=1.212-0.513\\\Rightarrow \lambda=0.699\ m[/tex]

[tex]\lambda=0.699\ m[/tex]

Average wavelength is given by

[tex]\frac{0.685+0.714+0.699}{3}=0.699\ m[/tex]

Average wavelength is 0.699 m

Average speed is given by

[tex]v=f\lambda\\\Rightarrow v=4.8\times 10^2\times 0.699\\\Rightarrow v=335.52\ m/s[/tex]

The average speed of sound is 336 m/s