Question

What is the correct expression of the standing wave equation?

• A. $\left(0.1\right)sin\left(\pi /2\right)xsin\left(10\pi \right)t$
• B. $\left(0.1\right)sin\left(\pi \right)xsin\left(10\pi \right)t$
• C. $\left(0.05\right)sin\left(\pi /2\right)xcos\left(10\pi \right)t$
• D. $\left(0.04\right)sin\left(\pi /\right)xsin\left(10\pi \right)t$

Answer 1

The correct option is A $\left(0.1\right)sin\left(\pi /2\right)xsin\left(10\pi \right)t$

$\mu =\frac{1.2}{2}=0.6kg/m$

$f=5Hz,\lambda =2l=4m$

$v=n\lambda =5\times 4=20m/s$

Using: $v=\sqrt{\frac{T}{mu}}\Rightarrow T={20}^2\times 0.6=240N$

$(\frac{\partial y}{\partial t}{)}_{max}=3.14m/s$

$\left(2A\right)\omega =3.14$

Amplitude, $2A=\frac{3.14}{2\times 3.14\times 5}=0.1m$

Equation of standing wave is: $y=0.1sin\left(\pi /2\right)\times sin\left(10\pi \right)t$