Chapter 11, Problem 9Q

To determine

Explain the difference between the speed of a transverse wave traveling along a cord and the speed of a tiny piece of the cord.

Answer to Problem 9Q

Solution:

The speed of the transverse wave is measuring how fast the wave disturbance moves along the cord and the speed of a tiny piece of the cord is measuring how fast the piece of cord moves perpendicularly to the cord, as the disturbance passes by.

For a uniform cord the speed is constant and fora tiny piece of the cord, it is not constant.

Explanation of Solution

The speed of the wave is how fast the disturbance moves along the cord and is constant for a uniform cord as long as the tension remains constant.

The speed of the transverse wave is measuring how fast the wave disturbance moves along the cord. For a uniform cord, that speed is constant, and depends on the tension in the cord and the mass density of the cord. The speed of a tiny piece of the cord is measuring how fast the piece of cord moves perpendicularly to the cord, as the disturbance passes by. That speed is not constant – if a sinusoidal wave is traveling on the cord, the speed of each piece of the cord will be given by the speed relationship for a simple harmonic oscillator, which depends on the amplitude and frequency of the wave.

Conclusion:

For a uniform cord the speed is constant and fora tiny piece of the cord, it is not constant.