Question

Traveling waves are generated on a string fixed at both ends. The string has a length L, a linear mass density m, and a tension T. Which of the following will cause the wave speed to increase?
I. Using the same string but increasing the tension.
II Using a longer string with the same μ and T.
III. Using a string with the same L and T but a smaller μ.

a. I only
b. II only
c. III only
d. I or II
d. I or III

Answer 1

Answer: d. I or II

Explanation: A traveling wave has speed that depends on characteristics of a medium. Characteristics like linear density (μ), which is defined as mass per length.

Tension or Force ($F_{T}$) is also related to the speed of a moving wave.

The relationship between tension and linear density and speed is ginve by the formula:

$|v|=\sqrt{\frac{F_{T}}{\mu} }$

So, for the traveling waves generated on a string fixed at both ends described above, ways to increase wave speed would be:

1) Increase Tension and maintaining mass and length constant;

2) Longer string will decrease linear density, which will increase wave speed, due to their inversely proportional relationship;

Then, ways to increase the wave speed is

I. Using the same string but increasing tension

II. Using a longer string with the same μ and T.