Question:

A wave equation which gives the displacement along the direction is given by $ y=0,001\text{ }sin\text{ }(100r+x) $ where, $ x $ and y are in metre and $ t $ in second. This equation represents a wave

Updated On: Jul 12, 2022
  • travelling with a velocity of 100 m/s in the negative $ x- $ direction
  • travelling with a velocity of $ \frac{50}{\pi } $ m/s in the positive $ x- $ direction
  • of wavelength 1 m
  • of frequency $ \frac{100}{\pi } $ Hz
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The Correct Option is A

Solution and Explanation

The standard equation of a wave, travelling with amplitude a in the negative $ x- $ direction with angular velocity $\omega$ is given by $ y=a\sin (\omega t+kx) $ ...(i) where, $ k $ is wave number. Given equation of wave is $ y=0.001\,\sin (100t+x) $ ..(ii) Comparing Eqs. (i) and (ii), we get $ v=\frac{\omega }{k}=\frac{100}{1} $ $ =100\,m/s $
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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