Question

A transverse wave is represented by y = A sin
(⍵????–????x). For what value of the wavelength is
the wave velocity equal to the maximum particle
velocity?
(a) ???? A (b) ???? A
2
(c) 2???? A (d) A

Answer 1

Answer:

The given equation is, y=Asin(ωt−kx)

Wave velocity, ν=

k

ω

.....(i)

Particle velocity, ν

p

=

dt

dy

=Aωcos(ωt−kx)

Maximum particle velocity, (ν

p

)

max

=Aω .....(ii)

According to the given question, ν=(ν

p

)

max

k

ω

=Aω (Using (i) and (ii))

k

1

=A or

2π

λ

=A (∵k=

λ

2π

)