Vibrations of rope tied by two rigid ends shown by equation y= 2 π t 2 π x , then minimum length of the rope will be

Correct answer: B. (1)/(2) m Equation of vibration aligned y & =1 2 π t 2 π x & =1 2 π (π x)/(1 / 2) aligned Comparing this equation with y=a 2 π (π x)/(λ) a=1Minimum length of string = (1)/(2) a= (1)/(2) × 1= (1)/(2) m

JIPMER 2014

Exam: JIPMER
Year: 2014
Subject: Physics
Chapter: Waves and Sound

JIPMER 2014 · Physics · Waves and Sound

Vibrations of rope tied by two rigid ends shown by equation y= 2 π...

Vibrations of rope tied by two rigid ends shown by equation

y=\cos 2 \pi t \sin 2 \pi x

, then minimum length of the rope will be

Options

A $1$ m
B $\frac{1}{2} m$
C $5$ m
D $2 \pi \mathrm{m}$

Correct answer

B. $\frac{1}{2} m$

Step-by-step solution

Equation of vibration

\begin{aligned} y & =1 \cos 2 \pi t \sin 2 \pi x \\ & =1 \cos 2 \pi \sin \frac{\pi x}{1 / 2} \end{aligned}

Comparing this equation with

y=a \cos 2 \pi \sin \frac{\pi x}{\lambda} \Rightarrow a=1Minimum length of

string =

\frac{1}{2}

\frac{1}{2}

\times 1=

\frac{1}{2}

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