A steel rod 100 cm long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod is given to be 2.53 kHz.

Question

(i) A steel rod 100 cm long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod is given to be 2.53 kHz. What is the speed of sound in steel?

(ii) A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly exited by a 430 Hz source? Will this same source be in resonance with the pipe if both ends are open? (Speed of sound = 340 m/s).

Answer 1

(i) For the fundamental mode,

λ = 2 L = 2 x 100 = 200 cm = 2m.

Frequency ν = 2.53 kHz = 2530 Hz

Speed of sound, v = νλ = 2530 x 2 = 5060 m/s

=5.06 km/s

(ii) Length of pipe L= 20 cm = 0.2 m

Speed of sound v= 340 m/s

Fundamental frequency of closed organ pipe

ν = v/4L = 340/4x0.2 = 425 Hz sw can be excited

Fundamental frequency of open organ pipe

Hence source of frequency 430 Hz will not be in resonance with open organ pipe.