Types of Waves Transverse and Longitudinal - UNSOLVED PRACTICE SET

Q7. Define a mechanical wave. What are the two essential conditions for the propagation of mechanical waves?

Q8. Distinguish between transverse waves and longitudinal waves with respect to:

(i) Direction of particle vibration

(ii) Examples in solids, liquids, and gases

(iii) Possibility of polarization

Q9. Why can't transverse waves travel through gases? Explain using the elastic properties of the medium.

Q10. Draw a labeled diagram showing one complete wavelength of:

(i) A transverse wave (label crest, trough, wavelength, amplitude)

(ii) A longitudinal wave (label compression, rarefaction, wavelength)

Q11. Explain why sound waves in air are longitudinal while waves on a stretched string are transverse.

Q12. Can a wave be both transverse and longitudinal at the same time? Give an example if yes, or explain why not.

Q13. With neat labeled diagrams, explain the formation and propagation of:

(i) Transverse waves on a stretched string

(ii) Longitudinal waves in a spring

For each, describe:

How the wave is produced

The direction of particle vibration

The direction of energy transfer

The regions of maximum and minimum displacement

Q14. Discuss the differences between mechanical waves and electromagnetic waves. For each type, explain:

(i) Whether a material medium is required

(ii) The nature of the wave (transverse/longitudinal/both)

(iii) Speed range and factors affecting speed

(iv) Examples from daily life

Also explain why electromagnetic waves can travel through vacuum while mechanical waves cannot.

Q15. A student sets up a slinky spring on a table to demonstrate wave motion.

(i) How should she move the end of the slinky to produce a transverse wave? Draw the shape of the spring.

(ii) How should she move the end to produce a longitudinal wave? Draw the shape of the spring.

(iii) In which case does the spring itself move forward with the wave?

(iv) She notices that the wave eventually dies out. What causes this? Name the phenomenon.

Q16. A wave on a string is described by the equation y = 0.02 sin(20πt – 10πx), where x and y are in meters and t is in seconds.

(i) Determine whether this wave is transverse or longitudinal. Justify.

(ii) Calculate the amplitude, wavelength, frequency, and speed of the wave.

(iii) Determine the direction of wave propagation.

(iv) Calculate the maximum particle velocity.

(v) Calculate the particle velocity at x = 0.1 m and t = 0.05 s.

Q17. A sound wave in air is represented by the displacement equation s = 0.001 sin(500πt – 1.5πx), where s is in meters.

(i) Identify this as a longitudinal or transverse wave. Explain.

(ii) Calculate the frequency, wavelength, and speed of the wave.

(iii) Calculate the maximum particle displacement velocity.

(iv) If the temperature of air increases by 20°C, how does the speed of this wave change? (No calculation needed, just explain)

Q18. In a school science exhibition, a student creates a wave demonstration using a rope of length 5 m and mass 0.5 kg, stretched with a tension of 20 N.

(i) Calculate the speed of transverse waves on this rope.

(ii) If the student generates a pulse at one end, how long does it take to reach the other end and return?

(iii) The student then fills a long metal pipe with water and strikes one end. Explain what types of waves travel through the water and through the metal.

(iv) Calculate the approximate time for a sound pulse to travel through 5 m of water. (Speed of sound in water ≈ 1500 m/s)

(v) Why does the sound pulse reach the other end faster through the metal pipe than through the water inside it?