The time period of a simple pendulum depends on:
A Mass of bob
B Length of string
C Amplitude
D Shape of bob
T=2πLgT = 2\pi \sqrt{\tfrac{L}{g}}T=2πgL; mass and amplitude (for small angles) do not affect TTT.
Which of the following is the correct condition for SHM?
A Restoring force ∝ velocity
B Restoring force ∝ displacement
C Restoring force ∝ – displacement
D Restoring force ∝ displacement²
SHM requires a restoring force proportional and opposite to displacement: F=−kxF = -kxF=−kx.
The time period of a simple pendulum depends on:
A Mass of bob
B Length of string
C Amplitude
D Shape of bob
T=2πLgT = 2\pi \sqrt{\tfrac{L}{g}}T=2πgL; mass and amplitude (for small angles) do not affect TTT.
The displacement in SHM is given by x=Acos(ωt)x = A \cos(\omega t)x=Acos(ωt). Maximum velocity equals:
A Aω2A\omega^2Aω2
B A/ωA/\omegaA/ω
C AωA\omegaAω
D AAA
Maximum velocity in SHM = AωA\omegaAω.
When displacement becomes maximum in SHM, acceleration is:
A Zero
B Maximum and positive
C Maximum and negative
D Minimum
At extreme positions, acceleration magnitude = a=−ω2xa = -\omega^2 xa=−ω2x, maximum and directed inward.
Energy in SHM is maximum in which form at mean position?
A Kinetic only
B Potential only
C Both K.E & P.E
D Zero
At mean position, displacement is 0 → P.E = 0 → K.E is maximum.
Frequency of SHM is:
A Inversely proportional to amplitude
B Independent of amplitude
C Directly proportional to amplitude
D Zero
Frequency depends only on system parameters (k, m), not amplitude.
A body of mass m executes SHM with spring constant k. Its period is:
A 2πkm2\pi\sqrt{\tfrac{k}{m}}2πmk
B 2πmk2\pi\sqrt{\tfrac{m}{k}}2πkm
C mk\sqrt{\tfrac{m}{k}}km
D 2πkm2\pi k m2πkm
Spring–mass oscillator: T=2πm/kT = 2\pi \sqrt{m/k}T=2πm/k.
Acceleration in SHM is maximum at:
A Mean position
B Halfway position
C Extreme positions
D At all positions equally
Acceleration ∝ displacement → maximum at extremes.
For SHM, the graph of acceleration vs displacement is:
A Parabolic
B Linear
C Circular
D Exponential
a=−ω2xa = -\omega^2 xa=−ω2x, a straight line with negative slope.
In SHM, velocity is zero at:
A Mean position
B All positions
C End positions
D Midway points
At extreme points, body momentarily stops → v=0v = 0v=0.
Damping force is proportional to:
A Displacement
B Velocity
C Mass
D Frequency
Damping force generally F=−bvF = -bvF=−bv.
In a lightly damped oscillator, the amplitude:
A Increases exponentially
B Stays constant
C Decreases exponentially
D Changes randomly
Light damping → amplitude decreases exponentially.
Resonance occurs when:
A Driving frequency = natural frequency
B Driving frequency = 2 × natural frequency
C Driving frequency = 0
D Natural frequency becomes zero
Resonance condition: fdrive=f0f_{\text{drive}} = f_0fdrive=f0.
Which statement is true for overdamped systems?
A Oscillate with increased amplitude
B Oscillate with decreased amplitude
C Do not oscillate
D Oscillate with same frequency
Overdamping prevents oscillation; motion returns slowly to equilibrium.
In forced oscillations, the phase difference between driving force and displacement at resonance is:
A 0°
B 45°
C 90°
D 180°
At resonance, displacement lags driving force by π\piπ radians.
In damped oscillation, the frequency:
A Increases
B Decreases
C Remains same
D Becomes zero
Damping reduces effective frequency: ωd<ω0\omega_d < \omega_0ωd<ω0.
Sharpness of resonance is measured by:
A Amplitude
B Q-factor
C Period
D Velocity
Larger Q → sharper resonance curve.
Coupled oscillators exchange:
A Frequency
B Momentum
C Energy
D Amplitude
Coupling allows periodic energy transfer.
In forced oscillations, amplitude depends on:
A Driving frequency
B Mass only
C Initial displacement only
D None
Response amplitude varies with driving frequency → resonance possible.
Damped oscillations eventually stop because:
A Energy is added
B Energy is lost
C Mass becomes zero
D Frequency increases
Energy is lost to friction or resistive forces.
A wave transports:
A Matter only
B Energy only
C Both matter and energy
D Neither
Waves transfer energy without net matter transport.
Speed of a wave on a string is given by:
A v=T/μv = \sqrt{T/\mu}v=T/μ
B v=Tμv = T\muv=Tμ
C v=T/μ2v = T/\mu^2v=T/μ2
D v=μ/Tv = \mu/Tv=μ/T
Wave velocity depends on tension T and linear density μ.
The relation between speed, frequency, wavelength is:
A v=fλv = f\lambdav=fλ
B v=f/λv = f/\lambdav=f/λ
C v=λ/fv = \lambda/fv=λ/f
D v=f2λv = f^2\lambdav=f2λ
Fundamental wave equation.
A transverse wave is one in which particles oscillate:
A Along direction of propagation
B Perpendicular to propagation
C At 45°
D Randomly
Transverse nature.
Which property changes when a wave passes from one medium to another?
A Frequency
B Time period
C Wavelength
D None
Frequency remains constant; speed changes → wavelength changes.
If wavelength doubles and frequency remains same, speed becomes:
A Half
B Double
C Four times
D Zero
v=fλv = f\lambdav=fλ: doubling λ doubles v.
Waves obey principle of superposition when:
A They are stationary
B Amplitude is large
C They overlap
D Medium is vacuum
Superposition applies to overlapping waves.
The energy of a wave is proportional to:
A Amplitude
B Amplitude²
C Frequency
D Wavelength
Energy ∝ A².
Wave front is a locus of points having:
A Minimum amplitude
B Same displacement
C Same phase
D Maximum energy
Defines points with identical phase.
A wave with zero particle displacement is a:
A Longitudinal wave
B Transverse wave
C Standing wave
D Shock wave
Standing waves have nodes (zero displacement points).
The distance between two consecutive nodes is:
A λ\lambdaλ
B λ/2\lambda/2λ/2
C λ/4\lambda/4λ/4
D 2λ2\lambda2λ
Nodes or antinodes occur at λ/2\lambda/2λ/2 intervals.
Antinode is a point of:
A Zero displacement
B Maximum displacement
C Zero energy
D Constant acceleration
Antinode experiences maximum oscillation.
In a closed organ pipe, fundamental frequency is:
A v/2Lv/2Lv/2L
B v/Lv/Lv/L
C v/4Lv/4Lv/4L
D 2v/L2v/L2v/L
Closed pipe supports odd harmonics → fundamental = v/4Lv/4Lv/4L.
In an open pipe, harmonics present are:
A Only even
B Only odd
C Odd multiples only
D All harmonics
Open pipes support all harmonics: v/2L,v/L,3v/2L,…v/2L, v/L, 3v/2L,\ldotsv/2L,v/L,3v/2L,…
A standing wave is formed due to:
A Single wave
B Reflection of a wave
C Interference of two identical waves moving oppositely
D Travelling waves only
Oppositely moving identical waves superpose → standing wave.
If length of string is L, fundamental wavelength is:
A L
B 2L
C L/2
D 4L
For string fixed at both ends: λ₁ = 2L.
For string vibration, number of antinodes in second harmonic is:
A 1
B 2
C 3
D 4
n-th harmonic has n antinodes.
Nodes are points where:
A Pressure is maximum
B Pressure is minimum
C Displacement is zero
D Frequency is zero
Node = no displacement.
In standing waves, energy flow between adjacent points is:
A Maximum
B Minimum
C Zero
D Infinite
Standing waves do not transport energy.
A harmonic is:
A Any integer multiple of fundamental frequency
B Only double the fundamental frequency
C Only odd multiples
D None
Harmonics = integer multiples of f₁.
Sound waves in air are:
A Transverse
B Longitudinal
C Electromagnetic
D Matter waves
In air, sound propagates via compressions & rarefactions → longitudinal.
Speed of sound is highest in:
A Air
B Water
C Vacuum
D Steel
Sound travels fastest in solids.
Doppler effect occurs due to:
A Change in wavelength only
B Relative motion between source and observer
C Change in amplitude
D Change in medium
Doppler shift arises from relative motion.
If source moves toward observer, frequency heard is:
A Lower
B Zero
C Higher
D Constant
Approaching source compresses waves → higher frequency.
Intensity of sound is proportional to:
A Amplitude
B Amplitude²
C Frequency
D Wavelength
Intensity ∝ amplitude².
Audible range of human ear is:
A 0–20 Hz
B 20–20,000 Hz
C 200–2000 Hz
D Above 20,000 Hz
Humans hear 20 Hz to 20 kHz.
Ultrasound refers to frequencies:
A Below 20 Hz
B 20–2000 Hz
C 2000–20,000 Hz
D Above 20,000 Hz
Ultrasound > 20 kHz.
Beats occur due to interference of two waves having:
A Same frequency
B Slightly different frequencies
C Different amplitudes only
D Zero phase difference
Beats occur when frequencies differ slightly.
The number of beats formed per second equals:
A Sum of frequencies
B Product of frequencies
C Difference of frequencies
D Ratio of frequencies
Beat frequency = |f₁ – f₂|.
Sound cannot travel through:
A Water
B Air
C Steel
D Vacuum
Sound needs a material medium; vacuum has none.