The equation overrightarrow{phi}(x, t) = over | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The given wave equation is $\overrightarrow{\phi}(x, t) = \overrightarrow{j} \sin \left( \frac{2\pi}{\lambda} vt \right) \cos \left( \frac{2\pi}{\

Vedclass · Accepted Answer

Transverse stationary wave

Vedclass · Answer

(D) The given wave equation is $\overrightarrow{\phi}(x, t) = \overrightarrow{j} \sin \left( \frac{2\pi}{\lambda} vt \right) \cos \left( \frac{2\pi}{\lambda} x \right)$.$1$. Stationary vs Progressive: $A$ wave is stationary if it has nodes (points where the amplitude is always zero). If we set $x = \frac{(2n+1)\lambda}{4}$ for $n = 0, 1, 2, \dots$,the term $\cos \left( \frac{2\pi}{\lambda} x \right)$ becomes zero. Since these points do not depend on time $t$,the amplitude remains zero at these positions. Thus,the wave is a stationary wave.$2$. Transverse vs Longitudinal: The displacement vector $\overrightarrow{\phi}$ is in the direction of $\overrightarrow{j}$ (the $y$-direction). The wave function depends on $x$,indicating propagation along the $x$-axis. Since the direction of vibration ($y$-axis) is perpendicular to the direction of propagation ($x$-axis),the wave is transverse.Therefore,the equation represents a transverse stationary wave. The correct option is $(D)$.

The equation $\overrightarrow{\phi}(x, t) = \overrightarrow{j} \sin \left( \frac{2\pi}{\lambda} vt \right) \cos \left( \frac{2\pi}{\lambda} x \right)$ represents:

Similar Questions

Two waves are approaching each other with a velocity of $20 \ m/s$ and frequency $n$. The distance between two consecutive nodes is

Write the amplitude and phase difference for all particles of the same interval for stationary waves.

Stationary waves are formed when

What is a refracted wave? $OR$ What is a stationary wave?

$A$ string fixed at both ends vibrates in a resonant mode with a separation of $2.0 \, cm$ between consecutive nodes. For the next higher resonant frequency,this separation is reduced to $1.6 \, cm$. The length of the string is .... $cm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module