Question

Pictured below is a standing wave pattern set up in a string by a vibrating source set at some fixed frequency.
The grey post is pulled to the right as indicated by the red arrow (increasing the tension in the string) until the next standing wave pattern appears. What is the wavelength of waves for this new pattern?
Assume that as the grey post is pulled, no appreciable change takes place in the distance between the frequency source and the post.

• A. $4.00m$
• B. $1.60m$
• C. $2.00m$
• D. $2.67m$
• E. $1.25m$

Answer 1

Answer: (B)

$1.60m$

Initially it is in its $4^{th}$ harmonic motion.

After increasing the tension, there appears next new pattern of $t^{th}$ harmonic motion.

$\therefore L=2\lambda +\frac{\lambda }{2}=\frac{5\lambda }{2}\Rightarrow L=4m=\frac{5\lambda }{2}\lambda =\frac{8}{5}[\lambda =1.6m]$is the new wavelength

Hence option (B) is correct