Exams › NEET › Physics › Waves
128 questions with worked solutions.
Q1. In stationary waves, nodes are the points where there is:
Answer: minimum displacement and maximum pressure change
In a stationary wave, nodes are points of zero displacement, so the particles there do not oscillate. For sound waves, pressure changes are largest at displacement nodes, making the correct choice minimum displacement and maximum pressure change.
Q2. How does the sound produced by a vibrating object in a medium reach your ear?
Answer: Through the vibration of particles
Sound travels through a medium by making its particles vibrate and pass the disturbance along from one particle to the next. That is why sound cannot travel in a vacuum and why the correct choice is the vibration of particles.
Answer: wavelength
The quantity described is the distance between successive points in the same phase of a wave. That is the definition of wavelength, and it applies to both traveling and standing waves.
Q4. An echo is simply a........of sound.
Answer: Reflection
An echo occurs when sound waves reflect off a surface and travel back to the listener. That makes it a reflection of sound, not a property like frequency or amplitude.
Q5. The condition for constructive interference is path difference should be equal to :
Answer: Integral multiple of wavelength
For constructive interference, the two waves must reinforce each other, which occurs when their phase difference is 0, 2π, 4π, etc. That corresponds to a path difference of nλ, where n is any integer.
Answer: Strain is maximum at nodes
In a stationary wave, nodes are points of zero displacement but the displacement changes most sharply there, so the spatial gradient is largest. Since strain is related to this gradient, it is maximum at nodes.
Answer: Sound travels faster in solid than in gas
Sound is a mechanical wave, so it needs a material medium to travel. It moves fastest in solids because particles are closely packed and transmit vibrations more efficiently than in gases.
Answer: 2.42 Å
A standing wave with 3 nodes and 2 antinodes corresponds to one full wavelength fitting between the two atoms. The distance between the atoms is 1.21 Å, which represents half a wavelength. Therefore, the full wavelength is 2 × 1.21 Å = 2.42 Å.
Answer: λ = πy₀/2
The maximum particle velocity is given by vmax = ωy₀, where ω = 2πv/λ. Setting vmax = 2v, we get 2πv/λ * y₀ = 2v. Simplifying, λ = πy₀/2.
Answer: 2.94 Hz
The time required to move from maximum displacement to zero displacement is one-fourth of the time period (T/4). Thus, T = 4 × 0.170 = 0.68 s. The frequency is given by f = 1/T = 1/0.68 ≈ 2.94 Hz.
Answer: 12 m
The frequency of the wave is given by f = 3600 waves / 60 s = 60 Hz. Using the wave speed formula v = fλ, we have λ = v / f = 960 m/s / 60 Hz = 16 m.
Q12. The equation of a wave is represented by: y = 10 sin [100t − x]. The velocity of the wave will be:
Answer: 100 m/s
The wave equation is of the form y = A sin(ωt − kx), where ω is the angular frequency and k is the wave number. The velocity of the wave is given by v = ω/k. Here, ω = 100 rad/s and k = 1 m⁻¹ (from the coefficient of x). Thus, v = 100/1 = 100 m/s.
Answer: 3.6
The wave equation is y = 60 cos(180t − 6x). The maximum particle velocity is given by ωA, where ω = 180 rad/s and A = 60 × 10⁻⁶ m. Thus, maximum particle velocity = 180 × 60 × 10⁻⁶ = 10.8 × 10⁻³ m/s. The wave velocity is v = ω/k = 180/6 = 30 m/s. The ratio of maximum particle velocity to wave velocity is (10.8 × 10⁻³) / 30 = 3.6 × 10⁻⁴. Hence, the correct answer is A) 3.6.
Q14. Which of the following equations represent a wave?
Answer: y = A sin (ωt − kx)
The equation y = A sin (ωt − kx) represents a wave because it includes both time (t) and position (x) in a sinusoidal form, which is characteristic of wave motion.
Answer: 10⁴ m/s
The given equation y = A sin(100t) cos(0.01x) represents a standing wave. The angular frequency ω = 100 rad/s and the wave number k = 0.01 rad/m. The wave velocity is given by v = ω/k = 100/0.01 = 10⁴ m/s.
Answer: 10/n
The distance between two consecutive nodes in a standing wave is half the wavelength (λ/2). The wavelength is given by λ = v/n, where v is the velocity and n is the frequency. Thus, the distance between two nodes is (v/n)/2 = 10/n.
Answer: 13.8 m
The frequency of the wave is calculated as f = (3600 waves) / (2 min × 60 s/min) = 30 Hz. Using the wave speed formula v = fλ, we find the wavelength λ = v / f = 760 m/s / 30 Hz = 25.3 m.
Answer: 4×10⁻⁴ m
The wavelength of sound is given by λ = v/f, where v is the speed of sound and f is the frequency. Substituting v = 1.7 × 10³ m/s and f = 4.2 × 10⁶ Hz, we get λ = (1.7 × 10³) / (4.2 × 10⁶) = 4 × 10⁻⁴ m.
Answer: Energy and linear momentum
In a longitudinal wave, energy and linear momentum are transmitted through the medium as the particles oscillate about their mean positions. Mass is not transported, as the particles only vibrate locally.
Q20. The frequency of sinusoidal wave y = 0.40 cos [2000 t + 0.80] would be
Answer: 1000 Hz
The angular frequency ω is given as 2000 rad/s. The frequency f is related to ω by the formula f = ω / (2π). Substituting ω = 2000, we get f = 2000 / (2π) = 1000 Hz.