Question

You are generating traveling waves on a stretched string by wiggling one end. If you suddenly begin to wiggle more rapidly without appreciably affecting the tension, you will cause the waves to move down the string:

A) at the same speed as before.
B) faster than before.
C) slower than before.

Answer 1

Answer:

B) Faster than before

Explanation:

By the time you begin to wiggle the string more rapidly you are indirectly increasing the number of cycles of the generated wave per second. This means that you are increasing the frequency of the generated wave.

Recall that the frequency of a travelling wave depends on the source of the wave.  You generating the wave  are the source of the wave.

The general relationship between velocity, frequency and wavelength is given by equation (1);

$v=\lambda f.....................(1)$

This shows a linear and direct relationship between velocity v and frequency f. That is to say that when frequency increases, velocity will also increase and vice versa.

As long as other factors such as the tension in the string remains constant, wiggling at a more rapid rate increases the frequency and which also increases the velocity, causing the wave to travel faster than before.