Question

wave is represented by y = a sin (At – Bx + C) where A, B, C are constants and t is in seconds & x is in metre. The Dimensions of A, B, C are- *v​

Answer 1

Given:

A wave is represented by the following equation:

$y = a \sin(At - Bx + C)$

To find:

Dimensions of A , B and C .

Calculation:

Trigonometric functions are always dimensionless.

Hence , we can say that :

• A × t will be dimensionless
• B × x will be dimensionless
• C will be dimensionless

$\therefore \bigg \{ A \times t\bigg \} = \bigg \{{M}^{0} {L}^{0} {T}^{0} \bigg \}$

$= > \bigg \{ A \times T\bigg \} = \bigg \{{M}^{0} {L}^{0} {T}^{0} \bigg \}$

$\boxed{ = > \bigg \{ A \bigg \} = \bigg \{{M}^{0} {L}^{0} {T}^{ - 1} \bigg \}}$

Similarly , we can say :

$\therefore \bigg \{ B\times x\bigg \} = \bigg \{{M}^{0} {L}^{0} {T}^{0} \bigg \}$

$= > \bigg \{ B\times L\bigg \} = \bigg \{{M}^{0} {L}^{0} {T}^{0} \bigg \}$

$\boxed{ = > \bigg \{ B\bigg \} = \bigg \{{M}^{0} {L}^{ - 1} {T}^{0} \bigg \}}$

Similarly, we can say :

$\boxed{\therefore \bigg \{ C \bigg \} = \bigg \{{M}^{0} {L}^{0} {T}^{0} \bigg \}}$

HOPE IT HELPS.

Answer 2

Explanation:

It will definitely help you