Question

A progressive wave is given by y = 10 Sin [2π(100t- 0.02x)]. Find the distance of separation between
two adjacent crests (x, y are in meters and t is in
second)
(1) 25 m
(2) 35 m
(3) 50 m
(4) 75 m​

Answer 1

Given :

▪ Wave equation of a progressive wave has been provided as given below.

$\underline{\boxed{\bf{\red{y=10\sin[2\pi(100t-0.02x)]}}}}$

• x and y are in meter
• t is in second

To Find :

▪ Distance between two adjacent crests.

Formula :

✒ A plane progressive harmonic wave travelling along positive direction at x-axis can be represented by

$\underline{\boxed{\bf{\green{y=A\sin 2\pi{\huge{(}}\dfrac{t}{T}-\dfrac{x}{\lambda}{\huge{)}}}}}}$

• $\lambda$ denotes wavelength
• A denotes amplitude
• x denotes distance of observation point from the origin
• t denotes time
• T denotes time period

▶ Distance between two adjacent crests is called as wavelength.

Calculation :

Comparing the given equation with wave equation, we get

→ x/$\lambda$ = 0.02x

→ 1/$\lambda$ = 0.02

→ $\lambda$ = 1/0.02

→ $\underline{\boxed{\bf{\purple{\lambda= 50m}}}}$