In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency $6\,Hz$. When tension in B is slightly decreased, the be at frequency increases to $7\,Hz$. If the frequency of A is $530\,Hz$, the original frequency of B will be :
- 523 Hz
- 524 Hz
- 536 H z
- 537 H z
The Correct Option is B
Solution and Explanation
Guitar string i.e. string is fixed from both ends
Frequency $\propto \sqrt{\text{Tension}}$
If tension in B slightly decrease then frequency of B decreases
If B is 536 Hz, as the frequency decreases, beats with A also decreases
If B is 524 Hz, as the frequency decreases, beats with A increases
If tension decreases, $f_{B}$ decreases and becomes $f'_{B}$
Now, difference of $f_{A}$ and $f'_{B}=7\,Hz$ (increases)
So, $f_{A}=f_{B}$
$f_{A}-f_{B}=6\,Hz$
$f_{A}=530\,Hz$
$f_{B}=524\,Hz$ (original)
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Concepts Used:
Waves
Waves are a disturbance through which the energy travels from one point to another. Most acquainted are surface waves that tour on the water, but sound, mild, and the movement of subatomic particles all exhibit wavelike properties. inside the most effective waves, the disturbance oscillates periodically (see periodic movement) with a set frequency and wavelength.
Types of Waves:
Transverse Waves -
Waves in which the medium moves at right angles to the direction of the wave.
Examples of transverse waves:
- Water waves (ripples of gravity waves, not sound through water)
- Light waves
- S-wave earthquake waves
- Stringed instruments
- Torsion wave
The high point of a transverse wave is a crest. The low part is a trough.
Longitudinal Wave -
A longitudinal wave has the movement of the particles in the medium in the same dimension as the direction of movement of the wave.
Examples of longitudinal waves:
- Sound waves
- P-type earthquake waves
- Compression wave