Sound in an Open Vertical Tube partially filled with Water

[fjccommish]

Homework Statement

An open vertical tube has water in it. A tuning fork vibrates over its mouth. As the water level is lowered in the tube, the seventh resonance is heard when the water level is 191.75 cm below the top of the tube.

a What is the wavelength of the sound wave? The speed of sound in air is 343 m/s. Answer in cm.

b What is the frequency of the sound wave (the tuning fork) in Hz?

c The water continues to leak out of the bottom of the tube. When the tube next resonates with the tuning fork, what is the length of the air column? Answer in cm.

Relevant Equations

L = [(2n-1)w]/4

w = wavelength, n is resonance #

I think this is correct. Please verify.

a

L = (2n-1)w/4 so w = 4L/13

w = 4(191.75)/13 = 59 cm

b

59cm is .59m

f = v/w = 343/.59 = appox 581.36 Hz

c

L =(2*8-1)*59/4 = 15*59/4 = 221.25cm.

 

[haruspex]

All looks good to me.

 

[fjccommish]

All looks good to me.

Thank you.

 

[Steve4Physics]

I think this is correct. Please verify.

Can I add this...

The question gives the length of the air column to 5 significant figures (191.75 cm) and the speed of sound to 3 sig. figs. (343 m/s).

Your answers should be rounded to 3 sig. figs.

(Getting this wrong in an exam’ could cost you a mark.)

 

[fjccommish]

Thanks.