Question

This question relates to standing waves.

A) Does a closed pipe have a higher or lower fundamental frequency than an open pipe of the same length?

B) If the length of an open tube is 0.8 m, experimentally find the: fundamental frequency and the frequencies of the third and fifth harmonic.

C) We have only addressed the variables of length, wave speed, harmonic number and frequency. These seem to be adequate to fully describe the frequency of a standing wave. But we know that when a musician tightens a guitar string, the frequency of the sound changes. Which of these independent variables changes value when a string is tightened?

Answer 1

A)

The fundamental frequency of an open pipe is

f = v / 2L

for closed pipe f = v / 4L

so an open pipe has higher fundamental frequency for same length

B)

for open pipe L = 0.8 m

f1 = v / 2L = 340 / (2*0.8)

f1 = 212.5 Hz

for 3rd harmonic means

f3 = 3 * f1

f3 = 3 * 212.5

f4 = 637.5 Hz

5th harmonic

f5 = 5 * f1 = 5 * 212.5

f6 = 1062.5 Hz

C)

As the string is tightened the length remains constant but

wave speed , harmonic number and frequency are changed