Question

A wave equation is given by
$ y = 4\,sin [\pi (\frac{t}{5} -\frac{x}{9} + \frac{1}{6})] $
where, $ x $ is in cm and $ t $ in second. which of the following is true ?

• A. $ \lambda = 18\,cm $
• B. $ v = 4\,m/s $
• C. $ a = 0.4 \,m $
• D. $ f = 50\,Hz $

Answer 1

Answer: (A)

Compare the given wave equation with standard one.
The given equation be written as
$y= 4 \,sin \,\left[\pi\left(\frac{t}{5} - \frac{x}{9} + \frac{1}{6}\right)\right] \quad...\left(i\right) $
The standard wave equation can be written as
$y=a \,sin \left(\omega t -kx + \phi\right) $
or $ y = a \, sin \left(\frac{2\pi}{T}t - \frac{2\pi}{\lambda} . x + \phi\right)\quad...\left(ii\right)$
Equating Eqs. $(i)$ and $(ii)$, we get
Amplitude
$a = 4 \,cm $
Frequency
$f = \frac{1}{T} = \frac{1}{10} Hz = 0.1 Hz $
Wavelength
$λ = 2 × 9 = 18 \,cm$
Velocity
$v = f λ = 0.1 × 18 = 1.8 \,cm/s$