Oscillations and Waves — Practice

Question 1

In simple harmonic motion, the acceleration of the particle at the mean position is:
(a) zero (b) maximum (c) equal to ω²A (d) infinite

Accepted Answer

(a) zero.

a = −ω²x, so at the mean position (x = 0) the acceleration is zero. It is maximum (ω²A) at the extremes.

Question 2

In simple harmonic motion, the speed of the particle is maximum at:
(a) the mean position (b) the extreme positions (c) half the amplitude (d) all points equally

Accepted Answer

(a) the mean position.

v = ω√(A² − x²) is largest when x = 0 (v_max = Aω) and zero at the extremes x = ±A.

Question 3

If the length of a simple pendulum is increased to 4 times its original value, its time period becomes:
(a) 2 times (b) 4 times (c) 16 times (d) √2 times

Accepted Answer

(a) 2 times.

T = 2π√(L/g) ∝ √L, so quadrupling the length multiplies the period by √4 = 2.

Question 4

A 2 kg mass on a spring of force constant 8 N/m executes SHM. Its time period is approximately:
(a) π s (b) 2π s (c) π/2 s (d) 4π s

Accepted Answer

(a) π s.

T = 2π√(m/k) = 2π√(2/8) = 2π√0.25 = 2π × 0.5 = π ≈ 3.14 s.

Question 5

If the amplitude of a body in SHM is doubled, its total energy becomes:
(a) 4 times (b) 2 times (c) 8 times (d) unchanged

Accepted Answer

(a) 4 times.

Total energy E = ½kA² ∝ A². Doubling the amplitude multiplies the energy by 2² = 4.

Question 6

A sound wave of frequency 500 Hz has a wavelength of 0.68 m. Its speed is:
(a) 340 m/s (b) 735 m/s (c) 500 m/s (d) 170 m/s

Accepted Answer

(a) 340 m/s.

v = fλ = 500 × 0.68 = 340 m/s.

Question 7

A sound of frequency 340 Hz travels in air at 340 m/s. Its wavelength is:
(a) 1 m (b) 0.5 m (c) 2 m (d) 340 m

Accepted Answer

(a) 1 m.

λ = v/f = 340/340 = 1 m.

Question 8

A body in SHM has a time period of 0.02 s. Its frequency is:
(a) 50 Hz (b) 20 Hz (c) 0.02 Hz (d) 100 Hz

Accepted Answer

(a) 50 Hz.

f = 1/T = 1/0.02 = 50 Hz.

Question 9

Two tuning forks of frequencies 256 Hz and 260 Hz are sounded together. The number of beats heard per second is:
(a) 4 (b) 2 (c) 8 (d) 516

Accepted Answer

(a) 4.

Beat frequency = |f₁ − f₂| = |256 − 260| = 4 beats per second.

Question 10

Which of the following is a longitudinal wave?
(a) Sound wave in air (b) Light wave (c) Wave on a string (d) Water surface ripple

Accepted Answer

(a) Sound wave in air.

Sound is longitudinal — the air oscillates along the direction of travel via compressions and rarefactions. Light and string waves are transverse.

Question 11

The time period of a simple pendulum does NOT depend on:
(a) the mass of the bob (b) its length (c) the acceleration due to gravity (d) both length and g

Accepted Answer

(a) the mass of the bob.

T = 2π√(L/g) contains only length and g — the mass of the bob (and, for small swings, the amplitude) does not affect the period.

Question 12

A string of length 1 m fixed at both ends carries transverse waves of speed 200 m/s. Its fundamental frequency is:
(a) 100 Hz (b) 200 Hz (c) 50 Hz (d) 400 Hz

Accepted Answer

(a) 100 Hz.

For a string fixed at both ends, f₁ = v/2L = 200/(2 × 1) = 100 Hz.

Question 13

In SHM, at a displacement equal to half the amplitude, the ratio of kinetic energy to potential energy is:
(a) 3 : 1 (b) 1 : 3 (c) 1 : 1 (d) 4 : 1

Accepted Answer

(a) 3 : 1.

KE ∝ (A² − x²) and PE ∝ x². At x = A/2: KE ∝ A² − A²/4 = 3A²/4 and PE ∝ A²/4, so KE : PE = 3 : 1.

Question 14

A pendulum clock keeping correct time on Earth is taken to the Moon, where g is one-sixth of Earth's. Its period will:
(a) increase by a factor of √6 (b) decrease by √6 (c) stay the same (d) increase by 6

Accepted Answer

(a) increase by a factor of √6.

T ∝ 1/√g. With g reduced to g/6, the period grows by √6 ≈ 2.45, so the clock runs slow on the Moon.

Question 15

As a sounding ambulance approaches a stationary observer, the frequency heard by the observer is:
(a) higher than the emitted frequency (b) lower (c) the same (d) zero

Accepted Answer

(a) higher than the emitted frequency.

An approaching source compresses the wavefronts, raising the observed frequency (pitch). As it passes and recedes, the pitch drops below the emitted value — the familiar siren effect.

Practice — Oscillations and Waves

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