Oscillations & Waves

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Q1. A tuning fork vibrates at a frequency of 440 Hz. What is the time period of the fork? (2020)

Solution:

Time period T = 1/f = 1/440 Hz ≈ 0.00227 s.

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Q2. A mass attached to a spring oscillates with a frequency of 2 Hz. What is the period of the oscillation?

Solution:

The period T is the reciprocal of frequency f. Thus, T = 1/f = 1/2 = 0.5 s.

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Q3. What is the frequency of a tuning fork that vibrates 256 times in 2 seconds? (2019)

Solution:

Frequency (f) = Number of vibrations / Time = 256 / 2 = 128 Hz.

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Q4. A pendulum swings with a maximum angle of 30 degrees. What is the approximate time period for small angles? (2022)

Solution:

For small angles, T ≈ 2π√(L/g). Assuming L = 1 m, T ≈ 2π√(1/9.8) ≈ 2.0 s.

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Q5. A pendulum of length 1 m swings with a small amplitude. What is its approximate time period? (2023)

Solution:

Time period (T) = 2π√(L/g) ≈ 2π√(1/9.8) ≈ 2 s.

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Q6. A wave has a frequency of 60 Hz and a wavelength of 3 m. What is its speed? (2016)

Solution:

Speed v = f × λ = 60 Hz × 3 m = 180 m/s.

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Q7. A wave pulse travels along a string and reflects off a fixed end. What happens to the wave upon reflection? (2021)

Solution:

When a wave pulse reflects off a fixed end, it inverts due to the boundary condition at the fixed end.

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Q8. A wave has a frequency of 50 Hz and a speed of 340 m/s. What is its wavelength? (2021)

Solution:

Wavelength λ is given by λ = v/f. Thus, λ = 340 m/s / 50 Hz = 6.8 m.

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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.

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Q10. 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.