The equation of a stationary wave is given by | vedclass

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

Question

(C) In the argument of the sine function,$\frac{2 \pi nt}{\lambda}$ must be dimensionless. Since $2\pi$ is dimensionless,the dimensions of $\frac{nt}{

Vedclass · Accepted Answer

The dimensions of $n/\lambda$ are $[T^{-1}]$.

Vedclass · Answer

(C) In the argument of the sine function,$\frac{2 \pi nt}{\lambda}$ must be dimensionless. Since $2\pi$ is dimensionless,the dimensions of $\frac{nt}{\lambda}$ must be $[M^0 L^0 T^0]$.This implies $[nt] = [\lambda] = [L]$. Thus,option $A$ is correct.Given $[nt] = [L]$ and $[t] = [T]$,we have $[n] = [L/T] = [LT^{-1}]$. Thus,option $B$ is correct.For the cosine function,$\frac{2 \pi x}{\lambda}$ must be dimensionless,so $[x] = [\lambda] = [L]$. Thus,option $D$ is correct.Now,consider the dimensions of $n/\lambda$. Since $[n] = [LT^{-1}]$ and $[\lambda] = [L]$,we have $[n/\lambda] = [LT^{-1}] / [L] = [T^{-1}]$.Option $C$ states the dimensions are $[T]$,which is incorrect. Therefore,option $C$ is the correct answer.

The equation of a stationary wave is given by $y = 2a \sin \left( \frac{2 \pi nt}{\lambda} \right) \cos \left( \frac{2 \pi x}{\lambda} \right)$. Which of the following statements is $NOT$ correct?

Similar Questions

If velocity $[V]$,time $[T]$,and force $[F]$ are chosen as the base quantities,the dimensions of mass will be:

Given that $v$ is the speed,$r$ is the radius,and $g$ is the acceleration due to gravity. Which of the following is dimensionless?

If the unit of force is $1 \,kN$,the unit of length is $1 \,km$,and the unit of time is $100 \,s$,what will be the unit of mass in $kg$?

Convert $1 \; \text{newton}$ ($SI$ unit of force) into $dyne$ ($CGS$ unit of force).

Vedclass Test Series

Exam Paper Generator

Online Exam Module