Question:

A source of sound gives 5 beats per second, when sounded with another source of frequency $100\, second^{-1}$ The second harmonic of the source, together with a source of frequency $205 \,second^{-1}$ gives 5 beats per second. What is the frequency of the source?

Updated On: Aug 16, 2024
  • $105\, second^{-1}$
  • $205 \,second^{-1}$
  • $95 \,second^{-1}$
  • $100 \,second^{-1}$
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The Correct Option is A

Solution and Explanation

Frequency of first source with 5 beats/sec = 100 and frequency of second source with 5 beats/sec = 205. The frequency of the first source = 100 $\pm$5 = 105 or 95 Hz. Therefore frequency of second harmonic source = 210 Hz or 190 Hz. As the second harmonic gives 5 beats/second with the sound of frequency 205 Hz, therefore frequency of second harmonic source should be 210 Hz. The frequency of source = 105 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