Wave Parameters Amplitude Wavelength Frequency - UNSOLVED PRACTICE SET

Q7. Define the following terms with their SI units:

(i) Amplitude

(ii) Wavelength

(iii) Frequency

(iv) Time period

(v) Angular frequency

(vi) Wave number

Q8. A wave has frequency 50 Hz and wavelength 4 m. Calculate its speed. If the frequency is doubled, what happens to the wavelength if speed remains constant?

Q9. Explain the difference between particle velocity and wave velocity. Which one depends on amplitude?

Q10. The equation of a wave is given by y = A sin(kx – ωt). Identify the physical quantities represented by A, k, ω, and the expression (kx – ωt).

Q11. A sound wave has frequency 1000 Hz and speed 340 m/s. Calculate its wavelength. How many complete waves pass a point in 1 second?

Q12. Draw a graph of displacement versus position for a sinusoidal wave at a fixed instant of time. Label amplitude, wavelength, crest, and trough.

Q13. A progressive wave is represented by y = A sin(kx – ωt + φ).

(i) Identify each symbol and state its physical meaning and SI unit.

(ii) Derive the relationship v = fλ from the wave equation.

(iii) Explain how the wave equation changes if the wave travels in the negative x-direction.

(iv) What is the significance of the phase constant φ?

Q14. Discuss the relationship between the various wave parameters. Starting from the basic definitions, show that:

(i) ω = 2πf = 2π/T

(ii) k = 2π/λ

(iii) v = ω/k = fλ

Draw graphs showing:

(a) Displacement vs position at fixed time (snapshot)

(b) Displacement vs time at fixed position

Label all important parameters on both graphs.

Q15. A student generates waves on a string using a vibrator. She observes that when the frequency is 20 Hz, the wavelength is 15 cm. She then changes the frequency.

(i) Calculate the speed of waves on the string.

(ii) If she increases the frequency to 40 Hz, what is the new wavelength?

(iii) If she decreases the frequency to 10 Hz, what is the new wavelength?

(iv) She notices that the amplitude also changes with frequency. Explain why this might happen.

Q16. A transverse wave on a string is described by y = 0.05 sin(4πt – 2πx), where x and y are in meters and t in seconds.

(i) Calculate the amplitude, wavelength, frequency, and time period.

(ii) Calculate the speed of the wave.

(iii) Calculate the maximum particle velocity.

(iv) Calculate the particle velocity at x = 0.25 m and t = 0.5 s.

(v) Sketch the wave profile at t = 0 and t = 0.25 s.

Q17. A tuning fork produces sound waves of frequency 512 Hz in air at 25°C. The speed of sound at 0°C is 331 m/s.

(i) Calculate the speed of sound at 25°C.

(ii) Calculate the wavelength of the sound wave at 25°C.

(iii) If the tuning fork is struck underwater (speed of sound in water = 1500 m/s), what is the new wavelength?

(iv) Does the frequency change when sound travels from air to water? Explain.

(v) Calculate the distance traveled by the wave in air in 2 seconds.

Q18. In a school physics lab, a student sets up a ripple tank to study water waves. The vibrator produces 20 ripples per second, and the student measures the distance between 5 consecutive crests as 12 cm.

(i) Calculate the frequency of the water waves.

(ii) Calculate the wavelength.

(iii) Calculate the speed of the water waves.

(iv) The student places a barrier with a small opening in the tank. What happens to the waves after passing through the opening? Name the phenomenon.

(v) If the student increases the frequency of the vibrator to 40 Hz while keeping the same wave speed, what happens to the wavelength? How would the diffraction pattern change?