A transverse wave on a string has amplitude A = 0.1 m and frequency f = 50 Hz. Maximum particle velocity is:
Answer: B
Maximum particle velocity = Aω = A(2πf) = 0.1 × 2π × 50 = 10π m/s
Q.382Medium
A sound source moves towards a stationary observer with velocity 30 m/s. The actual frequency of the source is 500 Hz and speed of sound is 330 m/s. The apparent frequency observed is:
A pipe closed at one end has a length of 50 cm. The fundamental frequency of the pipe is 170 Hz. What is the speed of sound in the pipe?
Answer: B
For a pipe closed at one end: f = v/(4L), so v = 4fL = 4 × 170 × 0.5 = 340 m/s
Q.384Medium
A wire of length 1 m and mass 10 g is fixed at both ends and has a tension of 90 N. What is the fundamental frequency of the wire?
Answer: A
f = (21L)√(T/μ) where μ = 0.101 = 0.01 kg/m. f = (21)√(090.01) = (21) × 300 = 150 Hz
Q.385Medium
A plane wave is incident on a boundary between two media. The angle of incidence is 30°. If the refractive index of the first medium is 1.5 and second is 1, what is the angle of refraction?
A tuning fork vibrates at 256 Hz. If the speed of sound is 340 m/s, the distance between consecutive compressions in the sound wave is:
Answer: B
λ = v/f = 256340 ≈ 1.33 m. Distance between consecutive compressions = wavelength = 1.33 m
Q.387Medium
A mechanical wave has the equation y = 5sin(2πx - 10πt), where x and y are in cm and t is in seconds. The wave velocity is:
Answer: A
Comparing with y = Asin(kx - ωt): k = 2π, ω = 10π. v = ω/k = 10π/2π = 5 cm/s
Q.388Medium
A sound wave undergoes total internal reflection at an interface. This indicates:
Answer: A
Total internal reflection occurs when a wave travels from a denser to a less dense medium at an angle greater than the critical angle
Q.389Medium
A sound source moves towards a stationary observer with velocity v_s. The observer hears frequency f'. The actual frequency of the source is f. The relationship is:
Answer: B
For source moving towards stationary observer: f' = f × v/(v - v_s), so f = f'(v)/(v + v_s) when rearranged
Q.390Medium
A wave on a string has amplitude A = 5 cm and period T = 0.2 s. The maximum velocity of a particle on the string is:
Two identical loudspeakers separated by 2 m emit sound of frequency 340 Hz in phase. If the speed of sound is 340 m/s, constructive interference occurs at:
Answer: D
Constructive interference occurs when path difference = nλ. λ = v/f = 340340 = 1 m, so path difference = 0, 1 m, 2 m, etc.
Q.392Medium
A pipe closed at one end has its fundamental frequency at 200 Hz. The next higher harmonic that can be produced is:
Answer: B
In a pipe closed at one end, only odd harmonics are produced: f, 3f, 5f, etc. Next higher = 3 × 200 = 600 Hz
Q.393Medium
A wave pulse travels along a rope. When it reaches a fixed end, the reflected pulse is:
Answer: B
At a fixed end, the reflected wave undergoes a phase change of 180° (or π radians) due to the fixed boundary condition
Q.394Medium
A progressive wave is represented as y = 2sin(100πt - πx/2). The phase difference between particles at x = 1 m and x = 3 m is:
Intensity I ∝ A²f² (or I ∝ A²ω²), both amplitude and frequency squared affect intensity
Q.396Medium
A wave undergoes refraction when passing from one medium to another. Which quantity remains constant?
Answer: C
During refraction, frequency remains constant as it depends on the source. Wavelength and velocity change due to change in medium properties
Q.397Medium
A string vibrates with 4 antinodes forming a standing wave pattern. The number of nodes (excluding ends) is:
Answer: A
For 4 antinodes (loops), there are 3 internal nodes. Pattern: node-antinode-node-antinode-node-antinode-node-antinode-node
Q.398Medium
A standing wave on a string has nodes at x = 0 and x = 2 m. The wavelength is:
Answer: C
Distance between two consecutive nodes = λ/2. If nodes are at 0 and 2 m, then λ/2 = 2, so λ = 4 m
Q.399Medium
Two sound waves have frequencies 256 Hz and 260 Hz. If they produce 4 beats per second, the beat frequency matches when:
Answer: B
Beat frequency = |f₁ - f₂| = 4 Hz only when waves overlap in the same region of space
Q.400Medium
An observer approaches a stationary sound source of frequency 500 Hz with velocity 20 m/s. If the speed of sound is 340 m/s, what is the observed frequency?
Answer: A
Using Doppler formula: f' = f(v + v_observer)/v = 500(340 + 20)/340 = 529.4 Hz
