1. 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?

2. 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]​?

3. 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.

4. 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?

5. 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?

6. 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?

7. 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?

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

9. 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?

10. 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?

11. 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?

12. 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?

13. 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.

14. 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.

15. A student blows across the open end of a narrow cylinder which is closed at the other end. If the length of the cylinder is $15.0cm$ and the speed of sound is 340 ms^−1, What is the frequency of the wave at the third harmonic?

16. 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?

17. 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?

18. 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?

19. 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?

20. A wave is incident on a boundary between two media, $X$ and $Y$. The wave travels faster in medium $Y$ than in medium $X$

Which of the following diagrams shows a possible path for this wave?

A.				B.
C.				D.

21. 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?

22. 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?

23. A car and a bicycle move in the same direction with speeds of v0​ and $v$ respectively as shown in the diagram below.

The car driver uses the horn to warn the cyclist. The frequencies of the sound heard by the car driver and cyclist are fo​ and $f$ respectively. Which of the following can be correct when f0?

• I.	v0=10 ms^−1 and v=5ms^−1
  II.	v0=5 ms^−1 and v=10ms^−1
  III.	v0=10 ms^−1 and v=10ms^−1

24. A light source approaches a stationary receiver at an increasing speed. The frequency of the emitted light is constant. Which graph shows how the observed frequency $f$ by receiver varies with the speed v of the light source?

A.			B.
C.			D.

25. 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??