### Q.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 s^{–1}).

**Answer:-**First (Fundamental); No

Length of the pipe, *l *= 20 cm = 0.2 m

Source frequency = *n*^{th} normal mode of frequency, ν_{n} = 430 Hz

Speed of sound, *v* = 340 m/s

In a closed pipe, the *n*^{th} normal mode of frequency is given by the relation:

Hence, the first mode of vibration frequency is resonantly excited by the given source.

In a pipe open at both ends, the *n*^{th} mode of vibration frequency is given by the relation:

**v**_{n} = *nv*/2*l*

*n* = 2l**v**_{n}/*v*