1. 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?

2. A $50cm$ string that is fixed at both ends produces a standing wave in the third harmonic. The speed of the wave on the string is 200 m s^−1

What is the frequency of oscillation?

3. The diagram shows a beam of light passing from medium $X$ to medium $Y$.

If the angle of incidence of the light increases, which of the following changes can be implemented to keep the angle of refraction the same?

4. The graph below shows the variation with displacement $x$ of the acceleration $a$ from the equilibrium position of a particle that undergoes simple harmonic motion.

The magnitude of the slope of the graph is directly proportional to

5. 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?

6. A microphone is emitting a sound wave with a wavelength of $15m$. Tom is $5m$ further away from the microphone than Mary. What is the phase difference of the sound wave, in radians, between them?

7. A body performs simple harmonic motion (shm). Which of the following could be the speed against the time graph for one period of motion?

A.				B.
C.				D.

8. 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?

9. A train is traveling at 30ms^−1 towards a stationary observer. It sounds a horn of frequency $450Hz$.

Which of the following statements is true about the observed frequency compared with the emitted frequency as the train approaches?

10. 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?

11. 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?

12. 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?

13. Two water waves with the same amplitude are traveling towards each other. The water level against the position graph of a water wave is shown below. The equilibrium water level is $5cm$.

What are the maximum and minimum water levels when the two waves overlap?

14. Two simple pendulums with lengths $16L$ and $9L$ have masses $4M$ and $M$ respectively. The period of the mass of $4M$ is T. What is the period of mass of $3M$?

15. 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?

16. A geostationary satellite is used for TV broadcasting. It orbits so that its position remains fixed above a receiver on earth. It undergoes circular motion with a speed of $v$ and the emitted frequency for a channel is f. Which of the following is correct?

17. 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?

18. For a body executing simple harmonic motion, which statement is not possible?

19. A taut string on a guitar is fixed at both ends.

What is [wavelength of fourth harmonic]/[wavelength of second harmonic] for the string?

20. The graph shows the variation with time $t$ of the displacement $s$ of an object suspended by a spring. At what time is the acceleration in the negative direction at a maximum??

21. A particle undergoes simple harmonic motion. Which of the following can be an expression of acceleration $a$ in terms of displacement $x$ and a constant value k?

22. 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]?

23. A light and a heavy spring are attached at point $Y$. A pulse was generated in the light spring and incident on the heavy spring. The positions of transmitted and reflected pulses after some time are as shown.

Which of the following is true about the incident pulse?

24.  

25. A speaker produces a sound near a pipe that is closed at one end by a movable piston. The piston is moved in the shown direction until a sound is first heard from the pipe. At this time, the length of the part of the tube near the speaker is $L$.

What is the distance moved by the piston to hear the next resonant sound from the pipe?