Question

The vibrations of a string fixed at both ends are described by the equation $y=\left(5.00mm\right)$ $\sin \left[\right(1.57c{m}^{-1}\left)x\right]\sin \left[\right(314s^{-1}\left)t\right]$. What are the wavelengths and the wave speeds of the two transverse waves that combine to give vibration?

• A. $4,2$
• B. $5,2$
• C. $4,3$
• D. $5,3$

Answer 1

The correct option is A $4,2$

From the given equation, the wave number $K=1.57c{m}^{-1}$ and angular frequency $\omega =314s^{-1}$, the wavelength is

$\lambda =\frac{2\pi }{k}=\frac{2\times 3.14}{1.57}$

$\lambda =4.00$ cm and the frequency is

$n=\frac{\omega }{2\pi }=\frac{314}{2\times 3.14}=50s^{-1}$

Now the wave speed is

$v=n\lambda =\left(50s^{-1}\right)\left(4.00cm\right)=2.00m/s$.