Question

A fellow student of mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x,t)=2.30mmcos[(6.98rad/m)x+(742rad/s)t]. Being more practical-minded, you measure the rope to have a length of 1.35 mm and a mass of 3.38 grams. Assume that the ends of the rope are held fixed and that there is both this traveling wave and the reflected wave traveling in the opposite direction.

What is the wave function y(x,t) for the standing wave that is produced?

Answer 1

Step-by-step explanation:

y(x,t)=2.30mmcos[(6.98rad/m)x+(742rad/s)t]

The angular velocity ω = 742 rad /s

wave function k = 6.98 rad /m

Amplitude A = 2.3 mm

y(x,t) = A cos( ωt + kx )

equation of wave reflected wave

y(x,t) = A cos( ωt - kx )

resultant standing wave

= y₁ +y₂

= A cos( ωt + kx ) +A cos( ωt - kx )

y(x,t) = 2 A cosωt cos kx

= 2 x 2.3 cos 742t .cos6.98x

= 4.6 mm . cos 742t .cos6.98x