Therefore the only frequencies that may be present are f,3f,5f, etc. Thus showing:in a pipe closed at one end only odd harmonics may be present.
SAMPLE PROBLEM 11A
The lowest pitch note produced by a pipe, open at both ends, is of frequency 512 Hz.What is the length of the pipe? The speed of sound in air is 340 m s1.
SAMPLE ANSWER 11A Step 1: Find the wavelength of the longitudinal travelling wave that creates the stationary wave.
c fLQL c f 340
512 85 128
Step 2: A pipe, open at both ends, has an antinode at both ends; therefore maximum distance between consecutive antinodes is the length of the pipe.
The distance between two consecutive antinodes is half the wavelength of the travelling wave. 2 Ql 85
The pipe is of length 33.2 cm. l L
2 128 85 256 0.3320
SAMPLE PROBLEM 11B
A guitar string of length 76 cm is set vibrating at its fundamental frequency, 278 Hz.What is the speed of sound in the string?
SAMPLE ANSWER 11B
Step 1: Find the wavelength of the transverse travelling wave that creates the stationary wave.The string has a node at either end; therefore maximum distance between consecutive nodes is the length of the string. The distance between two consecutive nodes is half the wavelength of the travelling wave.
l L 2 QL 2l 2(0.76) 1.52
Step 2: Find the speed of the wave in the string. The speed of sound in the string is 423 m s1.
