A wave travels with a velocity of 300 m/s and has a frequency of 150 Hz. What is its wavelength?
Using v = fλ, where v = 300 m/s and f = 150 Hz, λ = v/f = 150300 = 2 m
Which of the following is a characteristic of transverse waves?
In transverse waves, particle oscillation is perpendicular to the direction of wave propagation, such as in electromagnetic waves and ripples on water
A sound wave with frequency 500 Hz travels through air (speed = 330 m/s) and then enters water (speed = 1500 m/s). What happens to the wavelength?
Frequency remains constant during refraction. λ = v/f. Since speed increases from 330 to 1500 m/s, wavelength increases proportionally
Two waves of the same frequency interfere constructively. The resultant amplitude is:
In constructive interference, phase difference is 0° or 2πn. Resultant amplitude = A₁ + A₂
A stationary observer hears a sound from an approaching source. The observed frequency is:
Doppler effect: When source approaches observer, f' = f(v)/(v-vs), which is greater than f
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A string of length L is fixed at both ends. The fundamental frequency is f₁. What is the frequency of the second harmonic?
For a string fixed at both ends, fₙ = nf₁ where n is the harmonic number. Second harmonic (n=2) has f₂ = 2f₁
When two coherent light sources interfere, the condition for destructive interference is:
For destructive interference, the path difference must be odd multiples of λ/2: (2n+1)λ/2 or (n+21)λ
A wave equation is given as y = 5sin(2πx/4 - 2πt/2). The amplitude and frequency are:
From y = Asin(2πx/λ - 2πt/T), A = 5 m, and f = 1/T = 21π × 2π = 1 Hz
Standing waves are formed when:
Standing waves result from the superposition of two coherent waves traveling in opposite directions with the same frequency
The intensity of a sound wave is I. If the amplitude is doubled and frequency is halved, the new intensity will be:
Intensity ∝ A²f². New intensity = (2A)² × (f/2)² × I/(A²f²) = 4 × (41) × I = 2I
A pipe closed at one end and open at the other has a length of 0.5 m. The fundamental frequency is (speed of sound = 340 m/s):
For closed pipe, f₁ = v/(4L) = 340/(4×0.5) = 2340 = 170 Hz
Two sources of sound have intensities I₁ and I₂. The ratio of their amplitudes is:
Since I ∝ A², the ratio A₁/A₂ = √(I₁/I₂)
When a wave reflects from a denser medium, the phase change is:
Upon reflection from a denser medium (fixed end), there is a phase change of π radians or 180°
A transverse wave on a string has amplitude A, wavelength λ, and speed v. The maximum velocity of a particle is:
Maximum particle velocity = ωA = 2πfA = 2πA(v/λ) = 2πAv/λ
In Young's double slit experiment, if the distance between slits is d, distance to screen is D, and wavelength is λ, the fringe width is:
Fringe width β = λD/d, where D is the distance to the screen and d is the slit separation
A progressive wave y = 10sin(100πt - 0.01πx) cm is given. The wavelength is:
Comparing with y = Asin(2πft - 2πx/λ), we have 2π/λ = 0.01π, so λ = 200 cm
The velocity of a transverse wave on a string depends on:
Wave velocity v = √(T/μ), where T is tension and μ is mass per unit length. It is independent of frequency and amplitude
When a longitudinal wave travels through a medium, particles undergo:
In longitudinal waves, particles oscillate parallel to the direction of wave propagation, creating compressions and rarefactions
In a resonance tube experiment, the first resonance length is l₁ and second is l₂. The end correction is approximately:
For successive resonances in a resonance tube, l₂ - l₁ = λ/2, and end correction e ≈ (l₂ - l₁)/2 = λ/4
Two waves with intensities 4I and I interfere. The maximum intensity is:
I_max = (√I₁ + √I₂)² = (√(4I) + √I)² = (2√I + √I)² = (3√I)² = 9I
