Question

Consider the phase speed of transverse waves on a wire, with the changes listed below. Answer `true' (T), `false' (F), or `cannot tell' (C) to each of the five statements.
E.g., if the answer to the first statement is T and to the rest, F, enter TFFFF.

If the tension in the wire is doubled, the phase speed of the transverse wave decreases by a factor of square root of 2.

If the tension is increased, the length increased, and the mass of the wire is decreased, then the phase speed increases.

If the tension is increased and the mass of the wire is decreased (assuming the length remains the same), then the phase speed decreases.

If the length of the wire increases by a factor of 2 and the tension and mass remain the same, the phase speed of the transverse wave decreases by a factor of square root of 2.

If the mass of the wire is quadrupled and the tension and length remain the same, the phase speed of the transverse wave decreases by a factor of 2.

Answer 1

To answer all of these statements , we have to know the phase speed in terms of tension , length and mass
It is given by

Where T is tension , L is length and m is mass
Now
(1) False
If we double the tension then phase speed will increase not decrease
(2) True
on increasing tension and length phase speed will increase , since mass is in denominator therefore on decreasing it phase speed will increase.
(3) False
On increasing the tension and decreasing the mass will increase the phase speed not decrease it .
(4)False
it wil increase by factor of square root of 2
(5) True