Q44 of 118 Page 352

Find the greatest length of an organ pipe open at both ends that will have its fundamental frequency in the normal hearing range (20—20,000 Hz). Speed of sound in air = 340 m s-1.

Given:
Speed of sound in air



We are considering a minimum fundamental frequency of ,
since, for maximum wavelength, the frequency is a minimum.


Length of organ pipe


We have:




We know that:




On substituting the respective values in the above equation, we get:




Length of the organ pipe is 8.5 m.


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42

The first overtone frequency of a closed organ pipe P1 is equal to the fundamental frequency of an open organ pipe P2. If the length of the pipe P1 is 30 cm, what will be the length of P2?

 43

A copper rod of length 1.0 m is clamped at its middle point. Find the frequencies between 20 Hz and 20,000 Hz at which standing longitudinal waves can be set up in the rod. The speed of sound in copper is 3.8 km s-1.

 45

An open organ pipe has a length of 5 cm. (a) Find the fundamental frequency of vibration of this pipe. (b) What is the highest harmonic of such a tube that is in the audible range? Speed of sound in air is 340 m s-1 and the audible range is 20-20,000 Hz.

 46

An electronically driven loudspeaker is placed near the open end of a resonance column apparatus. The length of air column in the tube is 80 cm. The frequency of the loudspeaker can be varied between 20 Hz and 2 kHz. Find the frequencies at which the column will resonate. Speed of sound in air = 320 m s-1.