An IIT-JEE 2007 Question on Resonance Column

The following unusually simple MCQ appeared in IIT-JEE 2007 question paper:

In the experiment to determine the speed of sound using resonance column,

(a) prongs of the tuning fork are kept in a vertical plane

(b) prongs of the tuning fork are kept in a horizontal plane

(c) in one of the two resonances observed, the length of the resonating air column is close to the wave length of sound in air

(d) in one of the two resonances observed, the length of the resonating air column is close to half of the wave length of sound in air

As maximum possible displacement is to be imparted to the molecules of air in the resonance tube (for making the judgment of resonance condition easier), the prongs of the fork are to be kept such that they vibrate along the vertical direction (upwards and downwards). So, the correct option is (a).

You will find more multiple choice questions with solution at

physicsplus

Two Questions from Sound

(1) When two tuning forks are sounded together, 4 beats per second are produced. The frequency of one fork is 512Hz. When the other fork is loaded with a little wax, the beat frequency is 6Hz. The frequency of the other tuning fork is (in Hz)
(a) 516 (b) 514 (c) 512 (d) 508 (e) 502
This is a very simple question and you know that the beat frequency is the difference between the frequencies of the tuning forks. Since 4 beats are produced, the frequency of the other fork is either 516 or 508.
Loading of the other fork will reduce its frequency. So, if its actual frequncy is 516, the beat frequency is reduced. Since the beat frequency is increased, the actual frequency of the other fork must be 508 [option(d)].
Note that if the other fork is filed slightly, its frequency will be increased. If the question is modified this way and the beat frequency after filing is given as 6Hz itself, the answer will be option (a).
(2) The tension in a sonometer wire is increased by 96%. In order to keep the frequency of vibration of the wire unchanged, the length of the wire must be increased by
(a) 38% (b) 40% (c) 42% (d) 44% (e) 48%
The frequency of vibration of the wire is given by n = (1/2L)×√(T/m) where ‘L’ is the length, ‘T’ is the tension and and ‘m’ is the linear density of the wire. When T becomes 1.96T, the length L must become 1.4 L. The increment in L therefore is 40% [option (b)].