15.17 A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 430 Hz source? Will the same source be in resonance with the pipe if both ends are open? (speed of sound in air is 340 m/sec).

It is given in the question that:
Length of the pipe, l=20 cm=0.2 m 
Frequency of the source=nth normal mode of frequency, 
νn = 430 Hz  
Speed of sound, v=340 m/s
 In a closed pipe, the nth normal mode of frequency:
νn=(2n1)v4l; n is an integer=0, 1, 2, 3.....430=(2n1)3404×0.22n1=430×4×0.2340=1.012n=2.01n1
Hence, the first mode of vibration frequency is resonantly excited by the given source.
In a pipe open at both ends:
Since the number of the mode of vibration n has to be an integer, 
the given source does not produce a resonant vibration in an open pipe.