Question

A uniform long rope is suspended from the roof. A transverse wave pulse is produced at its lower end. As the wave travels upward along the suspended rope, then the
1) velocity of wave increases
2) wavelength of wave increases
3) frequency of wave remains constant

• A. only 1 and 2 are true
• B. only 2 and 3 are true
• C. only 1 and 3 are true
• D. 1, 2 and 3 all are true

Answer 1

Answer: (D)

1, 2 and 3 all are true

As the rope is heavy, the tension will be different at different points.
The frequency remains same as it depends on the source.
$V=\nu \lambda V=\sqrt{\frac{F}{\mu }}$
$F$ is the tension in the rope and $\mu$ is the mass rate.
$F$ varies, $\therefore$ $V$ varies and $\lambda$ varies.
In particular, the tension increases as we go up and correspondingly wavelength also increases.