1. A simple pendulum undergoes simple harmonic motion. The graph shows the variation of a quantity $y$ with horizontal displacement $x$ from the equilibrium position.

Which of the following quantities could be represented by quantity $y$?

2. A particle performs simple harmonic motion with a frequency of $0.05Hz$. The distance traveled by the particle in one complete oscillation is $16cm$. Which of the following graphs shows a correct variation of its position?

A.			B.
C.			D.

3. For an open pipe, the frequency of the first harmonic is $f$ and its wavelength is $\lambda$.

For a given harmonic of the same pipe, the ranges of motion of the particles in the pipe are shown below.

Three statements about the standing wave shown in this pipe are

I. The frequency is
II. The wavelength is λ/4
III. The wavelength is less than λ

Which statements are true?

4. Incident light of wavelength $600nm$ is emitted towards two slits separated by $1\mu m$. The interference pattern is observed on a wall. The distance between two adjacent maxima is $1.2m$. What is the distance of the wall from the slits?

5. For a wave traveling in a medium, the variation of the particles' displacement with distance travelled is shown in the following graphs, which represent the wave at different moments in time of a wave travelling to the right.

Graph I shows the wave at t=0 s, while graph II is at t=1s.

The time difference between the two graphs is less than the wave's period.

Graph I

Graph II

What is the wave speed?

6. A traveling wave is generated on a string tied to a speaker as shown.

Which of the following statements are correct about the travelling wave?

• I.	If the frequency of the sound decreases, the wavelength of the travelling wave increases.
  II.	If the speaker emits a louder sound the amplitude of the travelling wave increases.
  III.	If the frequency of the sound increases, the travelling wave moves along the string faster.

7. A thin beam of monochromatic blue light is incident upon a single slit barrier. The emerging light then passes through a double slit arrangement and falls on a screen some distance away.

An interference pattern is observed on the screen. In order to increase the distance between adjacent fringes, which of the following actions would be appropriate?

8. A mass-spring system rests on a frictionless surface. The mass is pulled to the right and released from a point $X$ at $t=0s$.

The mass executes simple harmonic motion between the points $X$ and $Y$. The mass reaches point Y for the first time at t=6s. Which of the following correctly shows directions of velocity and acceleration of the mass at t=10s?

9. A vibration generator with a frequency of $5Hz$ produces a travelling wave in a string. The graph shows how displacement of particles in the string varies with the distance from the source.

What is the wavelength and the speed of the wave?

10. An object with a mass of m is connected to a spring on a frictionless horizontal surface.

The object is displaced by $x$ from its equilibrium point $O$ to point $A$ and executes simple harmonic motion with a period of $T$. Which of the following are true if the object is displaced by $2x$?

11. Two identical objects $P$ and $Q$ are connected to identical springs. Both P and $Q$ are performing simple harmonic motion (SHM) around equilibrium level $O$.

The diagram shows positions of $P$ and $Q$ at time $t=0$. Which graph shows how kinetic energy of $P$ and Q vary with time t?

A.				B.
C.				D.

12. A monochromatic beam of light is incident on a double slit arrangement where the slit separation is 9.0×10^−5m and the slit-screen distance is 1.0m. The graph below shows the relative intensity of the light reaching the screen with respect to the distance from the central point of the pattern.

What is the wavelength of the light?

13. A traveling source produces sound waves nearby a child. The wavefronts of the sound waves and the position of a child are seen in the figure below.

The frequency of the generated sound waves is $f$. Which of the following is correct for both the direction of motion of the source and the observed frequency of the sound waves by the child?

14. A mass $M$ hangs in equilibrium on a spring. The mass is pulled down 10 $cm$ below the equilibrium position and released. It oscillates vertically about the equilibrium position, performing simple harmonic motion.

If it takes 0.5 $s$ after release to return to its equilibrium position, which of the following is true for its first oscillation?

15. Water drips onto a pond every 3.0 seconds. The speed of water waves in the pond has been measured to be 1.2m s^−1. What is the wavelength of the water waves generated because of the drops?

16. Wavefronts travel across a boundary between two media as shown.

Which of the following correctly describes the change, if any, in the speed, wavelength and frequency of the waves as they pass from across the boundary?

17. The bob on a conical pendulum is rotated at constant speed such that it describes a horizontal circle of diameter 15$cm$. A lamp is placed so that the shadow of the bob projected on a screen describes simple harmonic motion. What is the displacement of the shadow after the bob has traveled a total distance of 30$\pi$ cm?

18. A radio wave of frequency $90MHz$ travels a distance $d$. The number of wavelengths that can fit into this distance is 6000. What is $d$?

19. A mass-spring system executes simple harmonic motion with a period $T$ in a vertical plane. What is the period when the oscillating mass is doubled and the system is brought to a planet where the gravitational field strength at the surface is halved?

20. A fire truck’s siren emits a frequency of f0​. Starting from rest, it moves with constant acceleration and passes a stationary observer at t=to​. Which graph shows the variation of observed frequency f by the stationary observer with time?

A.			B.
C.			D.

21. A simple pendulum executing simple harmonic motion is released from one end and reaches equilibrium position in $2s$. Just after the equilibrium position, the length of the pendulum is reduced to one-fourth of its initial value because of wrapping around a nail.

What is the period of the simple pendulum?

22. A string fixed at both ends oscillates in a standing wave as shown with a wavelength of $400mm$.

What is the length of the string?

23. A boy tied two identical ropes to a fixed wall for a fitness exercise. He shakes the ropes to form waves.

A point on the right rope oscillates with a period of $0.4s$. A point on the left rope oscillates with a period of $0.2s$.

What is the ratio = [wavelength of right rope]/[wavelength of left rope]​?

24. A wave travels on a rope as shown, where $P$ is a point on the rope halfway between the equilibrium position and the maximum displacement.

Which is correct about the direction and magnitude of the velocity of point $P$ after half a period compared to the shown position?

25. Below are the graphs of the kinetic and potential energies against displacement $s$ for an object exhibiting simple harmonic motion.

Which of the positions marked on the axis represents the location of maximum speed?