SHM

Q. A transverse sinusoidal wave moves along a string in the positive $x-$direction at a speed of $10\text{cm/s}$. The wavelength of the wave is $0.5m$ and its amplitude is $10cm$. At a particular time $t$, the snap-shot of the wave is shown in figure. The velocity of point $P$ when its displacement is $0.05m$ is

1. $\frac{\sqrt{3}\pi }{50}\hat{j}\text{m/s}$
2. $-\frac{\sqrt{3}\pi }{50}\hat{j}\text{m/s}$
3. $\frac{\sqrt{3}\pi }{50}\hat{i}\text{m/s}$
4. $-\frac{\sqrt{3}\pi }{50}\hat{i}\text{m/s}$

Q. The equation of progressive wave in a wire is given by $y=0.15sin\left[2\pi (15t-\frac{x}{10})\right]$
Where the distance is in meters and time in seconds.
Determine i) amplitude, ii) frequency, iii) wavelength and iv) velocity of the wave

1. $A=0.15m,f=150Hz,v=150m/s,\lambda =1m$
2. $A=0.1m,f=15Hz,v=15m/s,\lambda =1m$
3. $A=0.15m,f=15Hz,v=150m/s,\lambda =10m$
4. $A=0.15m,f=30Hz,v=15m/s,\lambda =10m$

Q. A point mass oscillates along the $x-$axis according to the law $x=x_0\cos (\omega t-\pi /4)$. If the acceleration of the particle is written as $a=A\cos (\omega t+\delta )$, then

1. $A=x_0,\delta =-\pi /4$
2. $A=x_0{\omega }^2,\delta =\pi /4$
3. $A=x_0{\omega }^2,\delta =-\pi /4$
4. $A=x_0{\omega }^2,\delta =3\pi /4$

Q. The amplitude, speed and frequency of a plane progressive wave are respectively 0.05 m, 333 m/s, and 110 Hz. Write the equation of the wave.

1. $y=0.05sin110(t-\frac{x}{333})$
2. $y=0.05sin110\pi (t-\frac{x}{333})$
3. $y=0.05sin220(t-\frac{x}{333})$
4. $y=0.05sin220\pi (t-\frac{x}{333})$