Question

If = 3 sin (36 + 0.18 +/4) , find the amplitude and velocity of the wave.

Answer 1

$\huge\rm\red{Answer}$

Refer the attachment ♡...

Answer 2

Answer:

y(x,t)=asin(ωt+kx+ϕ) ... (i)

The given equation is:

y(x,t)=3.0sin(36t+0.018x+

4

π

) ...(ii)

On comparing both the equations, we find that equation (ii) represents a travelling wave, propgating from right to left.

Now using equations (i) and (ii), we can write:

ω=36 rad/s and k= 0.018 m

−1

We know that:

v=ω/2π and λ=2π/k

Also,

v=fλ

∴v=(ω/2π)×(2π/k)=ω/k

=36/0.018=2000cm/s=20m/s

Hence, the speed of the given travelling wave is 20 m/s.

(b) Amplitude of the given wave, a=3cm

Frequency of the given wave:

f=ω/2π=36/2×3.14=573Hz

(c) On comparing equations (i) and (ii), we find that the intial phase angle, ϕ=π/4

(d) The distance between two successive crests (or troughs) is equal to the wavelength of the wave.

Wavelength is given by the relation: k=2π/λ

∴λ=2π/k=2×3.14/0.018=348.89cm=3.49m