Waves
ICSE · Class 11 · Physics
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A wave has frequency 50 Hz and wavelength 2 m. What is its wave speed?
A wave travels at 340 m/s and has frequency 170 Hz. Find its wavelength.
A particle at the origin of a wave has amplitude 0.04 m and follows y = a sin ωt. What is its displacement when sin ωt = 1?
A wave has wavelength 0.8 m. Find its propagation constant k.
Sample Questions
A wave has period 0.2 s and wavelength 1.5 m. What is its speed?
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7.5 m/s
First find frequency using n = 1/T = 1/0.2 = 5 Hz. Then use v = nλ = 5 × 1.5 = 7.5 m/s. Two steps are needed.
A wave is written as y = 0.05 sin 2π(t/0.4 - x/1.2). What is its speed?
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3 m/s
Compare with y = a sin 2π(t/T - x/λ). Here T = 0.4 s and λ = 1.2 m. Use v = λ/T = 1.2/0.4 = 3 m/s, or v = nλ with n = 1/T = 2.5 Hz.
A particle at distance x = 0.75 m from the origin has phase lag φ = kx. If λ = 1.5 m, what is φ?
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π rad
Use k = 2π/λ = 2π/1.5 = 4π/3 rad/m. Then φ = kx = (4π/3) × 0.75 = π rad. So the phase lag is π rad.
Two particles in a wave are separated by 3 m. If the wavelength is 1.5 m, what is their phase difference?
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4π rad
Use Δφ = (2π/λ)Δx. Here Δx = 3 m and λ = 1.5 m. So Δφ = (2π/1.5) × 3 = 4π rad.
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