On a long, taut string a single crest is observed at the origin at time . At a later…

PHYSICS · Subjective · A Level · Physics · Waves · Waves

Problem

On a long, taut string a single crest is observed at the origin

x=0

at time

t=0

. At a later instant

t=0.04\,\text{s}

the same crest is found at

x=0.80\,\text{m}

. The wavelength of the wave travelling along the string is

1.60\,\text{m}

. (a) Determine the speed of the wave. (b) State clearly whether the wave propagates in the

+x

–direction or the

-x

–direction. (c) Using the data above, obtain a possible expression

y(x,t)=A\sin(kx\pm\omega t)

for the displacement of points on the string, taking the amplitude to be

2.0\,\text{cm}

and choosing the sign so that the equation matches the actual direction of travel.