Question 36: Waves

Question

A transverse wave on a string is described by $y=3 \sin (36 t+0.018 x+\pi / 4)$. 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)
$$ (\pi=3.14) $$

Accepted Answer

For a transverse wave, the standard form is
$$ y = A \sin(\omega t \pm kx + \phi) $$
Here, the given wave is
$$ y = 3 \sin(36t + 0.018x + \pi/4) $$
Comparing with the standard form, we get the wave number
$$ k = 0.018 	ext{ rad/cm} $$
The least distance between two successive crests is the wavelength $ \lambda $.
We know
$$ k = \frac{2\pi}{\lambda} $$
So,
$$ \lambda = \frac{2\pi}{k} $$
Substituting the values:
$$ \lambda = \frac{2 	imes 3.14}{0.018} $$
$$ \lambda = \frac{6.28}{0.018} $$
$$ \lambda \approx 348.89 	ext{ cm} $$
Nearest integer:
$$ \boxed{349} $$

Waves

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

Integer / Numeric Answer Type