Motion In A Plane

The speed of a wave on a string is given by the equation . We need to find the values of constants and such that this equation is dimensionally consistent.

We begin by analyzing the dimensions involved. The dimension of speed is . Given, the dimension of tension is . The mass per unit length has the dimension .

Substitute these into the equation:

Solving for the dimensions, we get:

Combining the dimensions, we have:

Set the powers of , , and equal to each other:

• For :
• For :
• For :

From , we get .

Substitute into :

.

Checking with other relation :

, which is correct.

Thus, the values of and are and , respectively. Hence, the correct option is:

.