A tuning fork of frequency $512\, Hz$ makes $4$ beats per second with the vibrating string of a piano. The beat frequency decreases to $2$ beats per sec when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was
- 510 Hz
- 514 Hz
- 516 Hz
- 508 Hz
The Correct Option is D
Solution and Explanation
$\therefore\, \, \upsilon_2=\upsilon_1\pm 4=512 \,Hz \pm 4$
$=516\, Hz$ or $508\, Hz$
Increase in the tension of a piano string increases its frequency
If $\upsilon_2=516 Hz, $ further increase in $\upsilon_2,$ resulted in an increase in the beat frequency. But this is not given in the question.
If $\upsilon_2=508\, Hz$, further increase in $\upsilon_2$ resulted in decrease in the beat frequency. This is given in the question. When the beat frequency decreases to $2$ beats per second. Therefore, the frequency of the piano string before increasing the tension was $508\, Hz$.
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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