The equation of stationary wave along a stretched string is given by y=5 (π x)/(3) 40 π t , where, x and y are in cm and t in second. The separation between two adjacent nodes is :

Correct answer: B. 3 cm Given, equation y=5 (π x)/(3) 40 π t Comparing with standard equation y=A k x ω t array rlrl & k & =(π)/(3) & (2 π)/(λ) & =(π)/(3) λ & =6 ~cm array Separation between two consecutive nodes =(λ)/(2)=(6)/(2)=3 ~cm

JIPMER 2006

Exam: JIPMER
Year: 2006
Subject: Physics
Chapter: Waves and Sound

JIPMER 2006 · Physics · Waves and Sound

The equation of stationary wave along a stretched string is given...

The equation of stationary wave along a stretched string is given by

y=5 \sin \frac{\pi x}{3} \cos 40 \pi t

, where,

x

and

y

are in cm and

t

in second. The separation between two adjacent nodes is :

Options

A1.5 cm
B3 cm
C6 cm
D4 cm

Correct answer

B. 3 cm

Step-by-step solution

Given, equation

y=5 \sin \frac{\pi x}{3} \cos 40 \pi t

Comparing with standard equation

y=A \sin k x \cos \omega t

\begin{array}{rlrl}\therefore & k & =\frac{\pi}{3} \\ \Rightarrow & \frac{2 \pi}{\lambda} & =\frac{\pi}{3} \\ \lambda & =6 \mathrm{~cm}\end{array}

Separation between two consecutive nodes

=\frac{\lambda}{2}=\frac{6}{2}=3 \mathrm{~cm}

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