A transverse sinusoidal wave on a string has a period t = 33.0 ms and travels in

Question

A transverse sinusoidal wave on a string has a period t = 33.0 ms and travels in the negative x direction with a speed of 30.0 m/s. At t = 0, a particle on the string at x = 0 has a transverse position of 2.00 cm and is traveling downward with a speed of 4.50 m/s. What is the amplitude of the wave m What is the phase constant rad What is the maximum transverse speed of the string m/s Write the wave function for the wave. (Use the form Asin(kx + wt + phi). Round all coefficients to three significant figures.) y(x, t) = The sound intensity at a distance of 18 m from a noisy generator is measured to be 0.22 W/m^2. What is the sound intensity at a distance of 27 m from the generator W/m^2

Explanation / Answer

Wave motion equation where a wavetravels to the -x direction,

y= A sin [k(x+ct)+p] where c- wave speed : k-wave vector= 2*pi/ l (l-wave length)

Now, since c=f*l

c= l/ T (T- time period) : k=2*pi/l= 2*pi/ (T*c)=6.347

initial conditions, at x=0,t=0 y=0.02 m

0.02= A sin p -----(1)

particle speed= dy/dt= A*k cos[ k(x-30t)+p]*(-30)

at t=0, 4.5=30*A*k cos p ------(2)

Solve (1) and (2)

(1)/(2) ; tan (p) =30k*0.02/4.5 =0.846

p=phase constant= 0.702 rad

from(1) 0.02= A*sin(0.702)

A= 0.031 m

speed= -30A*k cos[ k(x-30t)+p]

maximum speed= 30*A*k= 5.903 m/s

function fo the wave

y(x,t)=0.02 sin (6.35x-190.4t+0.702)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.