Q1. A wave travels through a medium with a speed of 500 m/s and has a wavelength of 5 m. What is its frequency? (2021)
Solution:
Frequency (f) = speed (v) / wavelength (λ) = 500 m/s / 5 m = 100 Hz.
⏱ Time: 0s
Q2. What is the frequency of a wave with a period of 0.01 s? (2020)
Solution:
Frequency f = 1/T = 1/0.01 s = 100 Hz.
⏱ Time: 0s
Q3. A sound wave travels at a speed of 340 m/s and has a frequency of 1700 Hz. What is its wavelength? (2021)
Solution:
Wavelength (λ) = Speed (v) / Frequency (f) = 340 m/s / 1700 Hz = 0.2 m.
⏱ Time: 0s
Q4. A mass-spring system oscillates with an amplitude of 0.1 m. What is the maximum speed of the mass if the angular frequency is 20 rad/s?
Solution:
The maximum speed v_max is given by v_max = Aω, where A is the amplitude and ω is the angular frequency. Thus, v_max = 0.1 * 20 = 2 m/s.
⏱ Time: 0s
Q5. If the amplitude of a simple harmonic oscillator is tripled, how does the total energy change? (2020)
Solution:
Total energy in SHM is proportional to the square of the amplitude. If amplitude is tripled, energy increases by 3^2 = 9 times.
⏱ Time: 0s
Q6. A wave has a frequency of 60 Hz and a wavelength of 1.5 m. What is its speed? (2022)
Solution:
Speed (v) = frequency (f) × wavelength (λ) = 60 Hz × 1.5 m = 90 m/s.
⏱ Time: 0s
Q7. A simple pendulum oscillates with a period of 2 seconds. What is the length of the pendulum? (2021)
Solution:
The period T of a simple pendulum is given by T = 2π√(L/g). Rearranging gives L = (T^2 * g) / (4π^2). Using g = 9.8 m/s² and T = 2 s, we find L = (2^2 * 9.8) / (4π^2) ≈ 1 m.
⏱ Time: 0s
Q8. A mass-spring system oscillates with a frequency of 1 Hz. What is the angular frequency? (2023)
Solution:
Angular frequency ω is related to frequency f by ω = 2πf. Therefore, for f = 1 Hz, ω = 2π(1) = 2π rad/s.
⏱ Time: 0s
Q9. What is the phase difference between two particles in the same medium oscillating in phase? (2023)
Solution:
If two particles are in phase, the phase difference is 0 radians.
⏱ Time: 0s
Q10. A wave travels through a medium with a speed of 500 m/s and has a wavelength of 2 m. What is its frequency? (2022)
Solution:
Using the wave equation v = fλ, we can find frequency f = v/λ = 500 m/s / 2 m = 250 Hz.
