If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is:

Question

Question

Answer 1

CONCEPT:

The speed v of the transverse wave is directly proportional to the square root of the tension and it is written as;

\(v \propto \sqrt T\)

Here, v is the speed and T is the tension.

CALCULATION:

As we know that;

\(v \propto \sqrt T\)

The initial tension of the string is written as;

\(v_1 \propto \sqrt T\) -----(1)

When the string is stretched, the initial tension is doubled.

\(v_2 \propto \sqrt {2T}\) -----(2)

Now, on dividing equation (1) by equation (2) we have;

\(\frac {v_1}{v_2} = \frac{1}{\sqrt2}\)

Hence option 4) is the correct answer.

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