The same frequency that causes a 0.25-m string to vibrate in its sixth harmonic also causes a 0.96-m pipe that is open at both ends to resonant in its second overtone. The speed of sound in air is 345 m/s. What is this common resonant frequency of the string and the pipe?

Question

anthonyym · Answer

I have for the string: 
lambda = L/3

v = lambda*f
f = (345m/s) / (0.25m/3) = 4140 Hz

For the pipe:
lambda = (2/3)L
f = (345m/s) / [(2/3)*0.96m] = 539 Hz

anthonyym · Answer

Update:
Am I not able to find the frequency for the string because I don't have the tension, linear density, and mass of the string by the formula
$$v=\sqrt{\frac{ T }{ m/L }}$$

fwizbang · Answer

You are given that the two frequencies are the same, so you only need to find it using the pipe.

parthkohli · Answer

Yeah, just calculate the frequency of the second overtone of the pipe and you're done.$$\frac{3v}{2L}$$