Wave Motion Flashcards
What are the two main types of mechanical waves?
Transverse and longitudinal waves.
What is the key difference between transverse and longitudinal waves?
In transverse waves, particles oscillate perpendicular to wave propagation; in longitudinal waves, particles oscillate parallel to wave propagation.
Give an example of a transverse wave.
Light waves, water waves.
Give an example of a longitudinal wave.
Sound waves, compression in a spring.
What is the difference between mechanical and electromagnetic waves?
Mechanical waves require a medium; electromagnetic waves do not.
Write the general form of a wave equation.
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Define the terms k, ω, and φ in the wave equation.
k: wave number, ω: angular frequency, φ: phase constant.
What is the relation between wave velocity (v), frequency (f), and wavelength (λ)?
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Derive wave velocity in terms of tension (T) and linear density (μ) for a string.
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How is wave speed affected by the medium?
Wave speed depends on the elastic and inertial properties of the medium.
State the principle of superposition.
When two or more waves overlap, the resultant displacement is the vector sum of the individual displacements.
What is constructive interference?
When waves combine to produce a larger amplitude.
What is destructive interference?
When waves combine to reduce or cancel the amplitude.
What is the condition for constructive interference?
Δx = nλ (where n is an integer).
What is the condition for destructive interference?
Δx = (n + 0.5)λ.
What are standing waves?
Waves formed due to the superposition of two identical waves traveling in opposite directions.
What are nodes in a standing wave?
Points of zero displacement.
What are antinodes in a standing wave?
Points of maximum displacement.
What is the fundamental frequency of a string fixed at both ends?
f₁ = v / 2L, where v is wave velocity and L is string length.
Write the formula for the n-th harmonic frequency in a stretched string.
f_n = n(v / 2L).
What is the first overtone in a string?
The second harmonic.
How do harmonics differ in closed and open pipes?
Closed pipes produce odd harmonics; open pipes produce all harmonics.
Write the fundamental frequency of a closed pipe.
f₁ = v / 4L.
What is the wavelength of the third harmonic in a closed pipe?
λ₃ = 4L / 3.
How does the length of the string or pipe affect the fundamental frequency?
Frequency is inversely proportional to length.
How does temperature affect the speed of sound?
Speed increases with temperature.
Write the formula for the speed of sound in air.
v = 331 + 0.6T (T in °C).
How does pressure affect the speed of sound in air?
Speed is independent of pressure (at constant temperature).
What is the relationship between intensity (I) and amplitude (A)?
I ∝ A².
Define the decibel scale.
A logarithmic scale to measure sound intensity.
Write the formula for sound level in decibels (L).
L = 10 log(I / I₀), where I₀ is the reference intensity.
What is the audible range for humans?
20 Hz to 20,000 Hz.
How does humidity affect the speed of sound in air?
Speed increases with humidity.
Why does sound travel faster in solids than in gases?
Higher elasticity and closer particle arrangement in solids.
What happens to wavelength when sound travels from air to water?
Wavelength increases as speed increases.
State the Doppler Effect.
Change in frequency or wavelength due to relative motion between source and observer.
Write the Doppler shift formula when the source moves toward the observer.
f’ = f (v + v₀) / (v - vₛ), where v is the speed of sound.
What happens to frequency if the source moves away from the observer?
Frequency decreases.
What is the Doppler Effect formula for light waves?
f’ = f (1 ± v/c), where v is relative velocity.
Name an application of the Doppler Effect.
Radar, medical ultrasound, astronomy.
How does the Doppler Effect differ for sound and light?
For sound, it depends on the medium; for light, it depends on relative velocity.
What happens to wavelength in the Doppler Effect when the source moves closer?
Wavelength decreases.
Define redshift.
Shift of light toward longer wavelengths when the source moves away.
Define blueshift.
Shift of light toward shorter wavelengths when the source moves closer.
In the Doppler Effect, what is vₛ?
Velocity of the source.
What is resonance?
When a system oscillates at its natural frequency due to an external periodic force.
Give an example of resonance.
Swinging in rhythm, tuning forks.
Why does resonance produce large amplitudes?
Energy transfer is maximized at the natural frequency.
What happens if the driving frequency is far from the natural frequency?
Amplitude decreases significantly.
Why is resonance important in musical instruments?
It amplifies specific frequencies, producing distinct sounds.
What is the relation between intensity and distance?
I ∝ 1/d² (Inverse square law).
What is the wavelength of a wave with frequency 500 Hz and speed 340 m/s?
λ = v / f = 340 / 500.
What is the phase difference between two points separated by one wavelength?
2π radians.
Define phase velocity.
The rate at which the phase of the wave propagates in space.
What is group velocity?
Velocity of the envelope of a wave packet.
What is a wavefront?
A surface of constant phase.
Define time period (T) of a wave.
Time for one complete oscillation.
Define frequency (f).
Number of oscillations per second.
How is power related to amplitude in a wave?
Power is proportional to A².
What is the speed of light in vacuum?
3 × 10^8 m/s.
What is sound?
Sound is a mechanical wave that propagates through a medium by particle vibration.
What type of wave is sound?
Longitudinal wave.
What is the frequency range of audible sound for humans?
20 Hz to 20,000 Hz.
What are infrasonic waves?
Waves with frequencies below 20 Hz.
What are ultrasonic waves?
Waves with frequencies above 20,000 Hz.
In which medium does sound travel fastest: solids, liquids, or gases?
Solids, due to higher elasticity.
Why can sound not travel in a vacuum?
Sound requires a medium for propagation.
How is sound produced?
By the vibration of an object, which creates compressions and rarefactions.
What is the relationship between sound intensity and amplitude?
Intensity is proportional to the square of the amplitude.
What is the wavelength of sound?
The distance between two consecutive compressions or rarefactions.
What is the speed of sound in air at 0°C?
331 m/s.
How does temperature affect the speed of sound?
Speed increases with temperature.
Write the formula for the speed of sound in air at temperature T.
v = 331 + (0.6 * T), where T is in °C.
How does the density of a medium affect the speed of sound?
Speed decreases with increasing density (for the same medium type).
How does elasticity of a medium affect the speed of sound?
Speed increases with higher elasticity.
Write the formula for the speed of sound in a medium.
v = √(K/ρ), where K is bulk modulus and ρ is density.
What is the speed of sound in water?
Approximately 1500 m/s.
What is the speed of sound in steel?
Approximately 5000 m/s.
Why does sound travel faster in humid air than in dry air?
Because water vapor is less dense than dry air, reducing overall density.
How does pressure affect the speed of sound in a gas?
At constant temperature, speed is independent of pressure.
What are the three main characteristics of sound?
Pitch, loudness, and quality (or timbre).
What determines the pitch of a sound?
Frequency of the sound wave.
What determines the loudness of a sound?
Amplitude of the sound wave.
What determines the quality or timbre of a sound?
Waveform or the mixture of frequencies.
How is loudness measured?
In decibels (dB).
Define intensity of sound.
Power per unit area, measured in watts per square meter.
Write the formula for the intensity of sound.
I = P / (4πr²), where P is power and r is distance from the source.
What is the threshold of hearing in terms of intensity?
1 × 10⁻¹² W/m².
Write the formula for sound level in decibels.
L = 10 log(I/I₀), where I₀ is the reference intensity.
How does the human ear distinguish between two sounds of the same pitch and loudness?
By their timbre or quality.
What is reflection of sound?
When sound waves bounce off a surface.
What is an echo?
A reflected sound wave heard after a time delay.
What is the minimum distance for an echo to be heard?
17.2 m (at 20°C) to allow a delay of 0.1 s.
What is reverberation?
Persistence of sound due to repeated reflections.
How is reverberation reduced in a room?
By using sound-absorbing materials like curtains and carpets.
What is refraction of sound?
Bending of sound waves when they pass from one medium to another.
What happens to the speed of sound during refraction from air to water?
Speed increases as sound enters water.
What is diffraction of sound?
The bending of sound waves around obstacles or through openings.
Why is diffraction more noticeable for sound than light?
Because sound has a longer wavelength than light.
What is the practical application of sound diffraction?
Hearing around corners.
What is the Doppler Effect?
Change in frequency or wavelength of sound due to relative motion between source and observer.
Write the formula for the Doppler Effect when the source moves toward the observer.
f’ = f (v + v₀) / (v - vₛ).
Write the formula for the Doppler Effect when the source moves away from the observer.
f’ = f (v - v₀) / (v + vₛ).
What is the observed frequency if the source is stationary and the observer moves toward it?
f’ = f (v + v₀) / v.
What happens to the frequency when the source and observer move away from each other?
Frequency decreases.
What is the Doppler Effect used for in medical applications?
Ultrasound to measure blood flow velocity.
What is redshift in the Doppler Effect?
Shift to lower frequency when the source moves away.
What is blueshift in the Doppler Effect?
Shift to higher frequency when the source moves closer.
Name a practical application of the Doppler Effect.
Speed radars for vehicles.
How does the Doppler Effect differ for sound and light waves?
Sound depends on the medium; light does not.
What is SONAR?
Sound Navigation and Ranging, used to detect objects underwater.
What is the principle of SONAR?
Reflection of ultrasonic waves.
Write the formula for distance calculation in SONAR.
d = vt, where v is wave velocity and t is time.
What is ultrasonic testing?
Using ultrasound to detect flaws in materials.
How are ultrasonic waves produced?
By piezoelectric crystals.
What is resonance in sound?
When an object vibrates at its natural frequency due to a periodic force.
Give an example of resonance in sound.
Vibrations in a guitar string.
How is sound used in cleaning applications?
Ultrasonic waves are used to clean delicate objects.
What is the application of sound in echocardiography?
Ultrasound imaging of the heart.
What is the speed of sound in vacuum?
Sound cannot travel in vacuum.
