Q52 of 118 Page 352

Show that if the room temperature changes by a small amount from T to T + ∆T, the fundamental frequency of an organ pipe changes from v to v + ∆v, where,


Let be the frequency of an open pipe at a temperature T. When the fundamental frequency of an organ pipe changes from to , the temperature changes from T to.


We know that:
----------- (i)


According to the question,



Applying this in equation (i), we get:




By expanding the right-hand side of the above equation using the binomial theorem, we get:


(Neglecting the higher terms)



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50

Consider the situation shown in figure (16-E9). The wire which has a mass of 4.00 g oscillates in its second harmonic and sets the air column in the tube into vibrations in its fundamental mode. Assuming

that the speed of sound in air is 340 m s, find the tension in the wire


 51

A 30.0-cm-long wire having a mass of 10.0 g is fixed at the two ends and is vibrated in its fundamental mode. A 50.0-cm-long closed organ pipe, placed with its open end near the wire, is set up into resonance in its fundamental mode by the vibrating wire. Find the tension in the wire. Speed of Sound in air = 340 m s-1.

 53

The fundamental frequency of a closed pipe is 293 Hz when the air in it is at a temperature of 20oC. What will be its fundamental frequency when the temperature changes to 22oC?

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A Kundt’s tube apparatus has a copper rod of length 1.0 m clamped at 25 cm from one of the ends. The tube contains air in which the speed of sound is 340 m/s. The powder collects in heaps separated by a distance of 50 cm. Find the speed of sound waves in copper.