The following MCQ which appeared in AIEEE 2003 question paper is worth noting:

**A metal wire of linear mass density 9.8 g/m is stretched with a tension of 10 kg wt between two rigid supports 1m apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency ‘n’. The frequency ‘n’ of the alternating current is **

**(a) 25 Hz (b) 50 Hz (c) 100 Hz (d) 200 Hz **

The wire vibrates because of the magnetic force on it. When the alternating current completes one cycle, the wire completes one oscillation and hence the frequency of oscillation of the wir is the same as the frequency of the alternating current (n). Therefore we have

n = (1/2L)√(T/m)** **where L is the length of the segment of the wire betweenetween the supports, T is the tension and ‘m’ is the linear density (mass per unit length) of the wire. Substituting for L, T and m we have

n = (½)√[(10×9.8)/(9.8×10^{–3} )] = 50 Hz.

The following MCQ is a conventional type:

**The displacement ‘y’ of a wave traveling in the X-direction is given by**

** y =10 ^{–4 }sin(600t – 2x + **

**π/3) metre,**

**where x is expressed in metre and t in seconds. The speed of the wave motion in ****ms**^{–1} is

**(a) 200 (b) 300 (c) 600 (d) 1200**** **

It will be useful to remember that the** **velocity of the wave, v = Coefficient of t /Coefficient of x. So, the correct option is (b).

Now consider the following MCQ on beats, which is of the type popular among question setters:

**A tuning fork of known frequency 256 Hz makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was**

**(a) 256 + 5 Hz (b) 256 + 2 Hz (c) 256 ****–**** 2 Hz (d) 256 ****–**** 5 Hz **

Since the beat frequency before increasing the tension in the piano wire was 5 Hz, the frequency of vibration of the piano wire was (256 ± 5) Hz. When the tension in the piano wire is increased, its frequency increases. If the original frequency of the piano wire was (256 + 5) Hz, the beat frequency would have increased on increasing the tension in the piano wire. Therefore, the original frequency of the piano wire was (256 – 5) Hz .

You will find more multiple choice questions (with solution) on waves at physicsplus: Multiple Choice Questions on Waves

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