Question

A wave is represented by y=asin(At-Bx+C);(A,B,C=Constants).The dimensions of aBC/A are as those of-
A)Velocity B)Length C)Mass D)Time

Answer 1

Answer on Question #41187, Physics, Mechanics | Kinematics | Dynamics

Question:

A wave is represented by $y = \frac{\text{asin}(At - Bx + C)}{(A, B, C = \text{Constants})}$. The dimensions of aBC/A are as those of-

- A) Velocity

- B) Length

- C) Mass

- D) Time

Answer:

The dimension of amplitude of wave $a$ is meter. $At$, $Bx$ and $C$ are dimensionless, therefore dimensions of $A$ and $B$ are:

$$[A] = \frac{1}{s}$$ $$[B] = \frac{1}{m}$$

Therefore:

$$\left[ \frac{aBC}{A} \right] = \left[ \frac{m \cdot \left(\frac{1}{m}\right)}{\frac{1}{s}} \right] = s$$

Second is dimension of time.

Answer: D) Time

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