Wave equation, superposition, beats, standing waves on strings and pipes.
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Q1 · Waves (Class 11 — ~20% weight) · EASY
Two waves travelling in the same direction are given by y1 = 0.05 sin(2π t - π x/6) and y2 = 0.05 sin(2π t - π x/6 + π/3), where x and y are in metres and t in seconds. The amplitude of the resultant wave is:
Q2 · Waves (Class 11 — ~20% weight) · MEDIUM
A string of length 1.5 m is fixed at both ends and vibrates in its fundamental mode. The speed of transverse waves on the string is 300 m/s. When the string vibrates in its third harmonic, the frequency of vibration is:
Q3 · Waves (Class 11 — ~20% weight) · HARD
Two tuning forks A and B produce 6 beats per second when sounded together. When fork B is loaded with a little wax, the number of beats per second decreases to 4. If the frequency of fork A is 320 Hz, the original frequency of fork B is:
Q4 · Waves (Class 11 — ~20% weight) · EASY
A sound wave of frequency 500 Hz travels in air with speed 350 m/s. After the wave completes 250 oscillations, what distance has the wave travelled?
Q5 · Waves (Class 11 — ~20% weight) · HARD
A sonometer wire of diameter d, density ρ₁ and under tension T vibrates with fundamental frequency n. Another wire of diameter 2d, density ρ₂ = ρ₁/2 under tension 3T has the same fundamental frequency n. What is the ratio of their lengths L₂/L₁?