(A) In the equation $y = a \sin(bt - cx)$,the argument of the sine function $(bt - cx)$ must be dimensionless.Therefore,the dimensions of $bt$ must be

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

(A) In the equation $y = a \sin(bt - cx)$,the argument of the sine function $(bt - cx)$ must be dimensionless.Therefore,the dimensions of $bt$ must be equal to the dimensions of $cx$.$[bt] = [cx]$$[b][T] = [c][L]$Rearranging this,we get the ratio $b/c = [L]/[T]$.Since $[L]/[T]$ represents the dimensions of velocity,the dimensions of $b/c$ are the same as those of wave velocity.

Class 11 Physics Units, Dimensions and Measurement Dimensional Analysis, Uses and Limitations

Medium

The displacement $y$ of a particle at a distance $x$ at time $t$ for a transverse wave is given by $y = a \sin(bt - cx)$,where $a, b,$ and $c$ are constants. The dimensions of $b/c$ are the same as those of:

A
Wave velocity
B
Wavelength
C
Amplitude of the wave
D
Wave frequency

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Units, Dimensions and Measurement

Subtopic

Dimensional Analysis, Uses and Limitations

If energy $(E)$,velocity $(v)$,and force $(F)$ are taken as fundamental quantities,what are the dimensions of mass?

Medium

View Solution

If force $(F)$,length $(L)$,and time $(T)$ are assumed to be fundamental units,then the dimensional formula of mass will be:

Medium

View Solution

Force $(F)$ and density $(d)$ are related as $F = \frac{\alpha}{\beta + \sqrt{d}}$. The dimensions of $\alpha$ and $\beta$ are:

Medium

View Solution

In a certain system of units,one unit of mass is $50 \ g$,one unit of length is $10 \ cm$,and one unit of time is $5 \ s$. Then,in this system,$1$ unit of pressure equals to :-

Medium

View Solution

$A$ physical quantity $X$ is given by $X = \frac{2 k^3 l^2}{m \sqrt{n}}$. The percentage errors in the measurements of $k, l, m,$ and $n$ are $1 \%, 2 \%, 3 \%,$ and $4 \%$ respectively. The percentage uncertainty in the value of $X$ is: (in $\%$)

EasyTS EAMCET 2023

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The displacement $y$ of a particle at a distance $x$ at time $t$ for a transverse wave is given by $y = a \sin(bt - cx)$,where $a, b,$ and $c$ are constants. The dimensions of $b/c$ are the same as those of:

Similar Questions

If energy $(E)$,velocity $(v)$,and force $(F)$ are taken as fundamental quantities,what are the dimensions of mass?

If force $(F)$,length $(L)$,and time $(T)$ are assumed to be fundamental units,then the dimensional formula of mass will be:

Force $(F)$ and density $(d)$ are related as $F = \frac{\alpha}{\beta + \sqrt{d}}$. The dimensions of $\alpha$ and $\beta$ are:

In a certain system of units,one unit of mass is $50 \ g$,one unit of length is $10 \ cm$,and one unit of time is $5 \ s$. Then,in this system,$1$ unit of pressure equals to :-

$A$ physical quantity $X$ is given by $X = \frac{2 k^3 l^2}{m \sqrt{n}}$. The percentage errors in the measurements of $k, l, m,$ and $n$ are $1 \%, 2 \%, 3 \%,$ and $4 \%$ respectively. The percentage uncertainty in the value of $X$ is: (in $\%$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module