Question

A guitar string is tuned by a tuning knob. Which of the following properties related to the vibrating string would remain constant as the tuning knob is turned?
I. Tension I the string
II. Frequency of standing waves in string
III. Wavelength of standing waves in the string
[A] I only
[B] III only
[C] I and II only
[D] II and III only
[E] I, II and III

Answer 1

Hint: In order to solve this question we need to understand sound waves. Sound waves are longitudinal waves which depend on the medium to propagate. Actually what happens is whenever we speak something or guitar tuned then it creates vibration in atoms in air surrounding it. So atoms vibrate about their mean position and hence collide with neighboring atoms which then vibrates so in this wave sound waves propagate and the pattern of vibration is termed as sound, it is recognized by our brain hence we can differentiate between sound of guitar and harmonium due to their different pattern of vibration.

Complete step-by-step solution:
Let Sound wave speed be “v”, its frequency be “f”, and its linear density be $\mu $
Also let the wavelength be $\lambda $ and $T$ be the tension in the string.
 We know speed of sound wave is given by, $v = \sqrt {\dfrac{T}{\mu }} $
So by changing the knob you are actually varying tension by loosening or tightening the string so if tension varies the speed varies.
Now we know relation between speed, frequency and wavelength as, $f\lambda = v$
So if speed varies then there are two possibilities: first is frequency and second wavelength varies.
Since the string length is always constant, so wavelength do not change
Hence frequency varies.
So the correct option is, [B] III only.

Note: It should be remembered that sound waves are the result of compression and rarefaction. Compression is defined as the phenomena when the atoms while vibrating come closer to each other and rarefaction is defined as phenomena when the atoms while vibrating are at maximum distance with each other.