A string under tension supports a wave whose displacement is given by y(x,t)=0.03 (4…

PHYSICS · Multi-part · CBSE · Physics · Waves · Waves

Problem

A string under tension supports a wave whose displacement is given by

y(x,t)=0.03\sin\bigl(4\pi x+200\pi t\bigr),

where

y

and

x

are in metres and

t

in seconds. (i) Find the displacement of the element of the string located at

x=0.50\,\text{m}

after

t=0.010\,\text{s}

. (ii) Determine whether the wave is travelling toward the positive

x

-direction or the negative

x

-direction. State the criterion used for your answer. (iii) Calculate the wavelength, frequency, and speed of this wave.