Question

✨✨Solve this..................


✨▪▪A transverse wave is produced in a string the maximum particle velocity is 3 m/s & the maximum particle acceleration is 9 m/s. If the wave velocity is 20m/s then find the wave equation.


▪▪Don't spam............... ​

Answer 1

Answer:

Let the equation of wave be y(x,t)=Asin(kx±ωt+ϕ)

we use ± here as no information is given about the direction of wave.

at any position x=x

o

, the velocity is given as

v(t)=dy(x

o

,t)/dt=Aωcos(kx

o

−ωt+ϕ)

and acceleration is given as

a(t)=dv(t)/dt=−Aω

2

sin(kx

o

−ωt+ϕ)

The ratio of magnitude of maximum velocity to maximum acceleration is

1/ω=3/90⇒ω=30

So maximum velocity magnitude is

Aω=3⇒A×30=3⇒A=0.1m=10cm

Now speed of wave is v=ν×λ=ω/k=20m/s

⇒k=30/20=3/2

So equation of wave is written as: y(x,t)=(10cm)sin(

2

3

x±30t+ϕ)