Choosing a title is way tougher than writing a problem

Classical Mechanics Level 1

When a wave traverse 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?

bt b/a cx y/a

2 solutions

Agent T
May 9, 2021

Y	[L]
A	[L]
Bt-cx	Dimensionless

$\dfrac{y}{a}=\dfrac{[L]}{[L]}=\text{dimensionless}$

Hence option $\boxed{b)}$ is correct

Boom!

Just like your infamous punchin' bag contraption problem, Agent-Tee........lazy, simple, and efficient!!! Have a great Sunday!

tom engelsman - 1 month ago

Haha ,agreed! XP Btw I've had a great Sunday :) And you too have a wonderful Monday/Sunday!

Agent T - 1 month ago

Tom Engelsman
May 8, 2021

In this sinusoidal function the quantity $bt-cx$ must be in radians (i.e. dimensionless). This rules out Choices A and C. The displacement $y$ is in units of distance, as well as the amplitude $a$ . Thus, Choice D is invalid. Finally, $b$ is in units of $\frac{1}{time}$ , which makes $\large \frac{b}{a} = \frac{1}{time \times distance} \Rightarrow$ Choice B is the correct answer.

Choosing a title is way tougher than writing a problem

2 solutions

Boom!

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