A transverse wave on a string is described by $y = 3\sin(36t + 0.018x + \pi/4)$ , where $x, y$ are in cm and $t$ in seconds. The least distance between the two successive crests in the wave is _____ cm. (Nearest integer)
( $\pi = 3.14$ )

Question

A transverse wave on a string is described by

y = 3\sin(36t + 0.018x + \pi/4)

, where

x, y

are in cm and

t

in seconds. The least distance between the two successive crests in the wave is _____ cm. (Nearest integer)
(

\pi = 3.14

)

Quantrex Academy · Accepted Answer

Correct answer: 0

The standard equation of a transverse wave is given by

y = A\sin(\omega t + kx + \phi)

Comparing this with the given equation

y = 3\sin(36t + 0.018x + \pi/4)

, we get the wave number

k = 0.018 \text{ cm}^{-1}

.

The least distance between two successive crests is the wavelength

\lambda

of the wave.

We know that

k = \dfrac{2\pi}{\lambda}

\lambda = \dfrac{2\pi}{k} = \dfrac{2 \times 3.14}{0.018}

\lambda = \dfrac{6.28}{0.018} = \dfrac{6280}{18} = 348.88 \text{ cm}

Rounding to the nearest integer, we get

349 \text{ cm}

.

Answer:

349

A transverse wave on a string is described by y = 3 (36t + 0.018x +...