Question

A standing wave in a pipe with a length $L=1.2m$ is described by $y(x,t)=y_0\sin [(2\pi /L)x]\sin [(2\pi /L)x+\pi /4]$ based on above information, which one of the following statemen tis incorrect?
(Speed of sound in air is $300m{s}^{-1}$)

• A. The pipe is closed at both ends
• B. The wavelength of the wave could be 1.2 m
• C. There could be a node at x = 0 and antinode at x = L / 2
• D. The frequency of the fundamental mode of vibrations is 137.5 Hz

Answer 1

Answer: (D)

Given speed of sound
$\upsilon =300m{s}^{-1}$
And wave equation is
$y=y_0\sin \left(\frac{2\pi }{L}x\right).\sin \left(\frac{2\pi }{L}x+\frac{\pi }{4}\right)$
So, angular wave number,
$k=\frac{2\pi }{\lambda }=\frac{2\pi }{L}$
$\therefore \lambda =L=1.2m$
Frequency of fundamental vibration is
$v=\frac{\upsilon }{\lambda }=\frac{300}{1.2}=250Hz$