Question

y(x, t) = A sin(300t + 0.01x + π/3)
a) What is the wave velocity ?
b) how does the phase of a particular location change after 0.01 s ?

Answer 1

Answer:

The equation of progressive wave travelling from right to left is given by the displacement function:

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

Answer 2

Explanation:

We know that

general equation of wave

y(x,t)=Asin(kx−ωt)

comparing this equation with given equation

1) A=0.005m → amplitude

k=80

ω=3

2) λ=

k

2π

=

80

2π

=(

40

π

)m

3) Time period T=

ω

2π

=

3

2π

sec

frequency f=

T

1

=

2π

3

Hz

4) Displacement at x=0.3m

t=20 sec

y=0.005sin(80×0.3−3×20)

=0.005sin(24−60)=0.005sin(−36)

=0.00495m

y=4.9mm.

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