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 wave has a speed of 300 m/s and a frequency of 150 Hz. What is its wavelength? (2022)

Solution:

Wavelength λ can be calculated using the formula λ = v/f. Therefore, λ = 300 m/s / 150 Hz = 2 m.

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Q3. 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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Q4. 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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Q5. A wave on a string is described by the equation y(x, t) = 0.05 sin(2π(0.1x - 5t)). What is the amplitude of the wave?

Solution:

The amplitude of the wave is the coefficient in front of the sine function. Here, the amplitude is 0.05 m.

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Q6. If the amplitude of a simple harmonic oscillator is increased, what happens to its total energy? (2021)

Solution:

The total energy (E) in a simple harmonic oscillator is given by E = (1/2)kA². If amplitude (A) increases, energy increases.

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Q7. What is the phase difference between two particles in a wave that are 1/4 wavelength apart? (2019)

Solution:

Phase difference (Δφ) = 2π × (distance / wavelength) = 2π × (1/4) = π/2 rad.

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Q8. A mass attached to a spring oscillates with a frequency of 2 Hz. What is the period of oscillation? (2023)

Solution:

Period (T) = 1 / Frequency (f) = 1 / 2 Hz = 0.5 s.

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Q9. 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.

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Q10. A sound wave travels through air at a speed of 343 m/s. If the frequency of the sound is 686 Hz, what is the wavelength? (2022)

Solution:

Using the wave speed formula v = f * λ, we can rearrange to find λ = v/f. Thus, λ = 343 m/s / 686 Hz = 0.5 m.