When a wave traverses a medium, the displacem | vedclass

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

Question

(D) Given the wave equation: $y = a \sin (bt - cx)$.In the trigonometric function $\sin(	heta)$, the argument $	heta$ must be dimensionless.Therefor

Vedclass · Accepted Answer

$\frac{b}{c}$

Vedclass · Answer

(D) Given the wave equation: $y = a \sin (bt - cx)$.In the trigonometric function $\sin(	heta)$, the argument $	heta$ must be dimensionless.Therefore, both $bt$ and $cx$ are dimensionless.$(a)$ $\frac{y}{a}$ is the ratio of two lengths, so it is dimensionless.$(b)$ $bt$ is the argument of the sine function, so it is dimensionless.$(c)$ $cx$ is the argument of the sine function, so it is dimensionless.$(d)$ The dimensions of $b$ are $[T^{-1}]$ and the dimensions of $c$ are $[L^{-1}]$.Thus, the dimensions of $\frac{b}{c} = \frac{[T^{-1}]}{[L^{-1}]} = [LT^{-1}]$, which represents the dimension of velocity.Therefore, $\frac{b}{c}$ is a quantity with dimensions.

When a wave traverses a medium, the displacement of a particle located at $x$ at a time $t$ is given by $y = a \sin (bt - cx)$, where $a, b,$ and $c$ are constants of the wave. Which of the following is a quantity with dimensions?

Similar Questions

If the buoyant force $F$ acting on an object depends on its volume $V$ immersed in a liquid,the density $\rho$ of the liquid,and the acceleration due to gravity $g$,then the correct expression for $F$ can be:

The force $F$ on a sphere of radius $a$ moving in a medium with velocity $v$ is given by $F = 6\pi \eta av$. The dimensions of $\eta$ are

$A$ and $B$ possess unequal dimensional formulas. Then,which of the following operations is not possible in any case?

In a measurement,it is asked to find the modulus of elasticity per unit torque applied on the system. The measured quantity has the dimension of $[M^a L^b T^c]$. If $b = 3$,the value of $c$ is . . . . . . .

Given that: $\lambda = a \cos \left( \frac{t}{p} - qx \right)$,where $t$ represents time in $s$ and $x$ represents distance in $m$. Which of the following statements is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module