MCQ
A sinusoidal wave of frequency $500 \,Hz$ has a speed of $350 \,m / s$. The phase difference between two displacements at a certain point at times $1 \,m$ apart is ...........
- A$\frac{\pi}{4}$
- B$\frac{\pi}{2}$
- ✓$\pi$
- D$\frac{3 \pi}{2}$
✓
Answer
Correct option: C.
$\pi$
c
(c)
(c)
$v=350 \,m / s \quad f=500 \,Hz$
$v=\frac{\omega}{k}$
$k=\frac{2 \pi f}{v}$
$k=\frac{2 \pi \times 500}{350}$
$k=\frac{2 \pi}{0.7}$
$\therefore \lambda=0.7 \,m$
Let equation of wave be
$y=A \sin (k x-\omega t)$
Let $x_1=0$ $x_2=1 \,m$
$y_1=A \sin (\omega t)$
$y_2=A \sin \left(\frac{2 \pi}{0.7} \times 1+\omega t\right)$
Hence phase difference $=\frac{20 \pi}{7}$ or approximately
Phase difference $\approx 3 \pi$
Which is same as $\Delta \phi=\pi$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Two blocks $A$ and $B$ of masses $6\, kg$ and $3\, kg$ rest on a smooth horizontal surface as shown in the figure. If coefficient of friction between $A$ and $B$ is $0.4$, the maximum horizontal force which can make them without separation is ........ $N$
→A small ball is projected up a smooth inclined plane with an initial speed of $10\ m/s$ along the direction at $30^o $ to the bottom edge of the slope. It returns to the edge after $2\, s$. The ball is in contact with the inclined plane throughout the process. ....... $^o$ is the inclination angle of the plane.
→A mass is performing vertical circular motion $($see figure$)$. If the average velocity of the particle is increased, then at which point is the maximum breaking possibility of the string:
→Which of the technique$(s)$ is/ are not used for measuring time intervals?
→Expansion during heating
A person walks $25.0^{\circ}$ north of east for $3.18 \,km$. How far would she have to walk due north and then due east to arrive at the same location?
→The range of a projectile for a given initial velocity is maximum when the angle of projection is ${45^o}$. The range will be minimum, if the angle of projection is ......... $^o$
→If $\overrightarrow{ P } \times \overrightarrow{ Q }=\overrightarrow{ Q } \times \overrightarrow{ P },$ the angle between $\overrightarrow{ P }$ and $\overrightarrow{ Q }$ is $\theta\left(0^{\circ} < \theta < 360^{\circ}\right) .$ The value of $\theta$ will be ........
→The velocity of a particle performing simple harmonic motion, when it passes through its mean position is
Sand is deposited at a uniform rate of $20\ kg/s$ and with negligible kinetic energy on an empty conveyor belt moving horizontally at a constant speed of $10$ meters per minute. Find the force required to maintain constant velocity of the conveyor belt.
→