Question

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

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

Answer 1

Answer: (A)

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