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

Question

When a wave traverses a medium the displacement of a particle located at x at a time is given by y = a sin (bt - cx), where a, and b are constants of the wave, which of the following is a quantity with dimensions? (A) (y/a)  (B) bt (C) cx (D) (b/c)

Tardigrade Admin · Accepted Answer

Given, y=a sin (b t-c x) Comparing the given equation with general wave equation y=a sin (2 π t/T)-(2 π x/λ) we get b=(2 π/T), c=(2 π/λ) (a) Dimensions of (y/a)=( text metre / text metre )=(L/L) (b) Dimensions of b t=(2 π/T) . t=(T/T) (c) Dimensions of c x=(2 π/λ) ⋅ x=(L/L) (d) Dimensions of (b/c)=(2 π/T) (2 π/λ)=(λ/T)=L T-1

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

$\frac{y}{a}$

$b t$

$c x$

$\frac{b}{c}$

Q. When a wave traverses a medium the displacement of a particle located at x at a time is given by y=asin(bt−cx), where a, and b are constants of the wave, which of the following is a quantity with dimensions?

ay​

bt

cx

cb​

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

$\frac{y}{a}$

$b t$

$c x$

$\frac{b}{c}$