Q49 of 118 Page 352

A U-tube having unequal arm-lengths has water in it. A tuning fork of frequency 440 Hz can set up the air in the shorter arm in its fundamental mode of vibration and the same tuning fork can set up the air in the longer arm in its first overtone vibration. Find the length of the air columns. Neglect any end effect and assume that the speed of sound in air = 330 m s-1.

Given:
Speed of sound in air
Frequency of the tuning fork


For the shorter arm:
Let the length of the shorter arm of the tube be .
Frequency of fundamental mode is given by:




On substituting the respective values, we get:




For the longer arm:
Let the length of the longer arm of the tube be .
Frequency of the first overtone


Frequency of the first overtone is given by:



On substituting the respective values, we get:




More from this chapter

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47

Two successive resonance frequencies in an open organ pipe are 1944 Hz and 2592 Hz. Find the length of the tube. The speed of sound in air is 324 m s-1.

 48

A piston is fitted in a cylindrical tube of small cross section with the other end of the tube open. The tube resonates with a tuning fork of frequency 512 Hz. The piston is gradually pulled out of the tube and it is found that a second resonance occurs when the piston is pulled out through a distance of 32.0 cm. Calculate the speed of sound in the air of the tube.

 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.