Question

An harmonic wave is travelling on a stretched string. At any particular instant, the smallest distance
between two particles having same displacement, equal to half of amplitude is 8 cm. Find the smallest
separation between two particles which have same values of displacement (magnitude only) egy
to half of amplitude.
a) 8 cm
b) 24 cm
c) 12 cm
d) 4 cm​

Answer 1

Answer:

$\huge\boxed{\fcolorbox{black}{pink}{Hi mate!}}$

An harmonic wave is travelling on a stretched string. At any particular instant, the smallest distance

between two particles having same displacement, equal to half of amplitude is 8 cm. Find the smallest

separation between two particles which have same values of displacement (magnitude only) egy

to half of amplitude.

a) 8 cm

b) 24 cm✔

c) 12 cm

d) 4 cm

Answer 2

The smallest seperation between two particles which have same values of displacement equal to half of magnitude is 4cm

1.consider all six particles have their displacement =±A/2

2.to get the separation between two particles having displacement of amplitude A/2,we have

A/2=Asin(kx-wt)

⇒kx=π/6,5π/6,....... and x2-x1=λ/3

3.now separation between two particles ie 1 and 2 comes out to be λ/3

from given λ/3=8cm

therefore λ=24cm

4.the separation between 1-3 -separation between 1-2

=λ/2-λ/3=λ/6=4cm