Chapter 16, Problem 1OQ

(a)

To determine

The speed of the wave.

Answer to Problem 1OQ

Option (a). It increases.

Explanation of Solution

Write the expression for the speed of the wave in terms of tension and mass per unit length.

  $\upsilon =\sqrt{\frac{T}{\mu }}$                                                                                                                      (I)

Here, $T$ is the tension, $\mu$ is the mass per unit length.

Substitute, $m$ is the mass, and $l$ is the length in equation (I), and take square on both sides.

  $\begin{array}{c}\upsilon =\sqrt{\frac{T}{\left(m/l\right)}}\\ {\upsilon }^2=\frac{Tl}{m}\end{array}$                                                                                                             (II)

From equation (II) it is clear that as mass of the rope decreases the speed of the wave increases. When the wave passes from massive string to less massive string the speed of the wave increases.

Conclusion:

Therefore, option (a) the right answer. As the wave propagates from massive to less massive string the speed of the wave increases.

(b)

To determine

The frequency of the wave.

Answer to Problem 1OQ

Option (c). It is constant.

Explanation of Solution

The frequency of the wave is remains constant. Since the rate at which crests come to the boundary is equal to the rate at which crests leave the boundary.

The frequency is independent of the mass of the medium through which it propagates. Thus, the frequency of the wave remains unchanged.

Conclusion:

Therefore, option (c) is the right answer. Thus the frequency of the wave remains when wave passes from massive string to less massive string.

(c)

To determine

The wavelength of the wave.

Answer to Problem 1OQ

Option (a). It increases.

Explanation of Solution

Write the expression for speed of the wave in terms of frequency and wavelength.

  $\upsilon =f\lambda$                                                                                                                      (II)

The speed of the wave increases when wave passes from massive string to less massive string. Since speed is proportional to the wavelength, as speed increase the wavelength is also increases.

Conclusion:

Therefore, option (a) is the right answer. The wavelength of the wave increases.