When a wave traverses a medium,the displaceme | 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.Therefore

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

Show that $\frac{\text{Joule}}{\text{meter}^2} = \frac{\text{Newton}}{\text{meter}}$.

Which of the following is dimensionally correct?

The force $F$ is given in terms of time $t$ and displacement $x$ by the equation $F = A \cos(Bx) + C \sin(Dt)$. The dimensional formula of $\frac{AD}{B}$ is -

If $x = a/t + b/t^2 + c$,where $x$ is the distance travelled by the body in metres and $t$ is the time in seconds,then the units of $b$ are:

If the force is given by $F = at + bt^2$ where $t$ is time,the dimensions of $a$ and $b$ are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module