Question

The displacement of a particle in standing wave on a string is given by $y(x,t)=0.4\sin \left(0.5x\right)\cos \left(30t\right)$, where $x$ and $y$ are in $\text{cm}$. Identify the incorrect option -

• A. Frequency of wave is $\frac{15}{\pi }\text{Hz}$
• B. Wave speed is $130\text{cm/s}$
• C. Amplitude of wave is $0.2\text{cm}$
• D. Wave number for the wave is $0.5{\text{cm}}^{-1}$

Answer 1

The correct option is B Wave speed is $130\text{cm/s}$

Given:
$y(x,t)=0.4\sin \left(0.5x\right)\cos \left(30t\right)$
On comparing with standard equation of standing waves,
$y(x,t)=2A\sin \left(kx\right)\cos \left(\omega t\right)$
We get,
Amplitude, $A=0.2\text{cm}$
Wave number, $k=0.5{\text{cm}}^{-1}$
Angular frequency, $\omega =30\text{rad/s}$
So, frequency, $f=\frac{\omega }{2\pi }=\frac{30}{2\pi }=\frac{15}{\pi }\text{Hz}$
Wave speed, $v=\frac{\omega }{k}=\frac{30}{0.5}=60\text{cm/s}$