A transverse wave propagating along x -axis is represented by y(x, t)=8.0 (0.5 π x-4 π t-π / 4) where x is in metres and t is in seconds. The speed of the wave is:

Correct answer: A. 8 ~m / s It is given that: y ( x_1 t)=8.0 (0.5 π x-4 π t- (λ)/(9)) Compare this equation with standard equation y=a ((2 π x)/(λ)- 2 π t T +φ) we have aligned (2 π)/(λ)& =0.5 π λ & =(2 π)/(0.5 π)=4 m (2 π)/(T)& =4 π T & =(1)/(2) U=(1)/(T)& =(1)/(y_2)=2 H_ 2 . aligned

NEET 2006

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

NEET 2006 · Physics · Waves and Sound

A transverse wave propagating along x -axis is represented by y(x,...

A transverse wave propagating along

x

-axis is represented by

y(x, t)=8.0

\sin (0.5 \pi x-4 \pi t-\pi / 4)

where

x

is in metres and

t

is in seconds. The speed of the wave is:

Options

A $8 \mathrm{~m} / \mathrm{s}$
B $4 \pi \mathrm{m} / \mathrm{s}$
C $0.5 \pi \mathrm{m} / \mathrm{s}$
D $\frac{1}{2} \mathrm{~m} / \mathrm{s}$

Correct answer

A. $8 \mathrm{~m} / \mathrm{s}$

Step-by-step solution

It is given that: y

\left(

x_1 t\right)=8.0 \sin

\left(0.5 \pi

x-4

\pi

\frac{\lambda}{9}\right)

Compare this equation with standard equation y=a \sin

\left(\frac{2 \pi x}{\lambda}-\frac{2 \pi t}{\mathrm{ T}}+\phi\right)

we have

\begin{aligned}\frac{2 \pi}{\lambda}& =0.5 \pi\\ \Rightarrow \quad \lambda & =\frac{2 \pi}{0.5 \pi}=4 \mathrm{ m}\\ \frac{2 \pi}{T}& =4 \pi\\ \Rightarrow \quad T & =\frac{1}{2} \sec\\ U=\frac{1}{T}& =\frac{1}{y_2}=2 \mathrm{H}_{2} . \end{aligned}

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