Question

Question: On a certain day, the speed of sound is 335 m/s. A frequency of 531 Hz is played near an open pipe. The length of the pipe can be adjusted. Part 1) What length should the pipe be set to in order to hear the 7th harmonic? 1= m Part 2) In reality there are end effects. These can be approximated as 0.600 x r where r is the radius of the pipe at each open end. The antinode occurs this distance outside the pipe. The pipe in this question has a radius 5.34 cm. What length should the pipe really be in order to hear the 7th harmonic? = m Part 3) What is the fundamental frequency when the pipe is set to this length? (The length found in the second part.) f= Hz Check

Answer 1

(1) Fundamental frequency = f_o = 531 Hz.

Speed of sound in air = v = 335 m / s.

Hence, wavelength of the fundamental is $\lambda$ _o = v / f_o = ( 335 / 531 ) m = 0.63 m = 63 cm.

So, length of the pipe for producing the 7^th harmonic = L = 7$\lambda$_o / 2 = 220.5 cm.

(2) Total end correction for both sides = 2 x 0.6r = 1.2 x 5.34 cm = 6.408 cm.

Hence, length of the pipe should be L = 220.5 cm + 6.408 cm = 227 cm.

(3) Fundamental wavelength of the sound, when the pipe is L = 227 cm long, is :

$\lambda$_o = 227 cm x 2 / 7 = 64.86 cm 0.6486 m.

Hence, fundamental frequency is now f_o = v / $\lambda$ _o = ( 335 / 0.6486 ) Hz = 516.5 Hz.