Question:
A wave is expressed by the equation $ y= a\,sin [\frac{\pi x}{2a} - \frac{\pi t}{2}]$ where $x$ and $y$ are in $m$ and $t$ in $s$. The distance travelled by the wave in $3 \,s$ is
A wave is expressed by the equation $ y= a\,sin [\frac{\pi x}{2a} - \frac{\pi t}{2}]$ where $x$ and $y$ are in $m$ and $t$ in $s$. The distance travelled by the wave in $3 \,s$ is
Updated On: Jul 5, 2022
- $a$
- $2a$
- $3a$
- $4a$
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The Correct Option is C
Solution and Explanation
The given wave equation is
$y=a\, sin \left(\frac{\pi x}{2a} - \frac{\pi t}{2}\right) \quad...\left(i\right)$
The standard wave equation is
$y=a \,sin \left(kx- ax\right) \quad...\left(ii\right) $
$k =\frac{\pi}{2a}, \omega = \frac{\pi}{2} $
The speed of the wave is
$ \upsilon= \frac{\omega}{k} = \frac{\frac{\pi}{2}}{\frac{\pi}{2a}} = a$
Distance travelled by the wave in $3\, s$ is
$=\upsilon t = a\left( 3\right) = 3a$
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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