Question

Equation of progressive wave is \hspace25mm y = A \sin \big(10 \pi x + 11 \pi t + \frac{\pi}{3}.

• A. its wavelength is 2 units
• B. it is travelling in the positive x-direction
• C. wave velocity is 1.5 units
• D. time period of SHM is 1 s

Answer 1

Answer: (A)

its wavelength is 2 units

Answer 2

The standard equation is
\hspace30mm y = a \sin \, 2 \pi \big(\frac{t}{T} - \frac{x}{\lambda} + \phi \big) \hspace35mm ....(i)
Dividing and multiplying the given equation by 2$\pi$, we get
\hspace30mm y= a \sin \, 2 \pi \big(\frac{10}{2}x + \frac{11}{2}t + \frac{\pi}{3} \hspace35mm ....(ii)
On comparing Eqs. (i) and (ii), we get
\hspace30mm \lambda = 2 units