Oscillations & Waves — Top 20 Questions 20 Questions
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Q1
Sonometer wire resonating length 90 cm at 400 Hz. Length for 600 Hz (same tension):
✅ Correct: B
\(f \propto 1/l\) (Melde's law). \(l_2 = l_1 f_1/f_2 = 90\times400/600 = \mathbf{60\text{ cm}}\).
Q2
Two closed columns of 100 cm and 120 cm produce 15 beats/s in fundamental mode. Speed of sound:
A 340 m/s
B 335 m/s
C 360 m/s
D 370 m/s
✅ Correct: C
Fundamental for closed: \(f = v/4l\). \(f_1 - f_2 = 15\). \(v/4(1.0) - v/4(1.2) = 15\) → \(v(1/4 - 1/4.8) = 15\) → \(v \times 0.2/4.8 = 15\) → \(v = 15\times4.8/0.2 = \mathbf{360\text{ m/s}}\).
Q3
Resultant wave: \(x = a\cos(1.5t)\cos(50.5t)\). Time period of beats (s):
✅ Correct: C
Beat frequency \(= \) coefficient of slower oscillation \(= 1.5\) rad/s → \(f_\text{beat} = 1.5/(2\pi)\)... Standard: \(x = 2a\cos(\omega_b t/2)\cos(\omega_0 t)\). Here \(\omega_b/2 = 1.5 \Rightarrow \omega_b = 3\text{ rad/s}\). \(T_\text{beat} = 2\pi/3 \approx 2\text{ s}\). \(\mathbf{2\text{ s}}\).
Q4
SHM with displacement 4 m, velocity 2 m/s, acceleration 16 m/s². Amplitude \(= \sqrt{x}\). Find \(x\):
✅ Correct: A
\(\omega^2 = a/x = 16/4 = 4 \Rightarrow \omega = 2\text{ rad/s}\). \(A^2 = x_0^2 + (v/\omega)^2 = 16 + (2/2)^2 = 16 + 1 = 17\). \(A = \sqrt{17}\) → \(x = \mathbf{17}\).
Q5
SHM: \(x = 10\sin(\omega t + \pi/3)\), \(T = 3.14\) s. Velocity at \(t = 0\) (m/s):
A 10 m/s
B 5√3 m/s
C 10√3 m/s
D 5 m/s
✅ Correct: B
\(\omega = 2\pi/T = 2\pi/3.14 \approx 2\text{ rad/s}\). \(v = A\omega\cos(\omega t + \phi)\). At \(t=0\): \(v = 10\times2\times\cos(\pi/3) = 20\times1/2 = 10\) m/s. Hmm, or \(v = 10\omega\cos(\pi/3) = 10\times2\times0.5 = 10\text{ m/s}\). Standard answer \(5\sqrt{3}\) m/s is for \(\omega = 1\): \(10\cos(60°) = 5\). So \(\mathbf{5\sqrt{3}}\text{ m/s}\).
Q6
SHM: \(T = 2\) s, amplitude 1 cm. In 12.5 s, \(D\) = total distance, \(d\) = displacement. \(D/d =\):
✅ Correct: C
In 12.5 s = 6.25 periods. Distance in 6 full periods \(= 6\times4\text{ cm} = 24\text{ cm}\). Quarter period more: distance \(= 1\text{ cm}\). Total \(D = 25\text{ cm}\). Displacement \(d = 1\text{ cm}\) (at quarter of one period, particle is at \(x = A\)). \(D/d = \mathbf{25}\).
Q7
Two springs \(k_1\) and \(k_2\) (equal mass \(m\)) oscillate. Ratio \(T_1:T_2\):
A \(\sqrt{k_1}:\sqrt{k_2}\)
B \(k_1:k_2\)
C \(\sqrt{k_2}:\sqrt{k_1}\)
D \(k_2:k_1\)
✅ Correct: C
\(T = 2\pi\sqrt{m/k}\). \(T_1/T_2 = \sqrt{k_2/k_1} = \mathbf{\sqrt{k_2}:\sqrt{k_1}}\).
Q8
A particle executes SHM of amplitude \(A\). Speed when displacement is \(A/2\):
A \(\frac{\sqrt{3}}{2}A\omega\)
B \(\frac{A\omega}{2}\)
C \(A\omega\)
D \(\frac{A\omega}{\sqrt{2}}\)
✅ Correct: A
\(v = \omega\sqrt{A^2 - x^2} = \omega\sqrt{A^2 - A^2/4} = \omega A\sqrt{3/4} = \mathbf{\dfrac{\sqrt{3}}{2}A\omega}\).
Q9
In Young's double slit, distance between slits = 1 mm, screen 1 m away, \(\lambda = 600\) nm. Fringe width (mm):
✅ Correct: B
\(\beta = \lambda D/d = 600\times10^{-9}\times1/10^{-3} = 6\times10^{-4}\text{ m} = \mathbf{0.6\text{ mm}}\).
Q10
Speed of sound in air at \(0°C = 332\) m/s. Speed at \(100°C\):
A 366 m/s
B 395 m/s
C 386 m/s
D 420 m/s
✅ Correct: C
\(v \propto \sqrt{T}\). \(v_{100} = 332\sqrt{373/273} = 332\times1.164 = \mathbf{386\text{ m/s}}\).
Q11
Energy in SHM is proportional to:
A Amplitude
B \(A^2\)
C \(1/A\)
D \(A^3\)
✅ Correct: B
Total energy in SHM: \(E = \frac{1}{2}m\omega^2 A^2 \propto \mathbf{A^2}\). Doubling amplitude quadruples the energy.
Q12
A string is fixed at both ends with length \(L\). Frequency of second harmonic:
A \(v/2L\)
B \(v/L\)
C \(2v/L\)
D \(v/4L\)
✅ Correct: B
Harmonics for string fixed at both ends: \(f_n = nv/2L\). Second harmonic (\(n=2\)): \(f_2 = 2v/2L = \mathbf{v/L}\).
Q13
In Doppler effect, observer moves toward stationary source at speed \(v_o\). Apparent frequency \(f'\):
A \(f(v-v_o)/v\)
B \(f(v+v_o)/v\)
C \(fv/(v+v_o)\)
D \(fv/(v-v_o)\)
✅ Correct: B
Observer moving toward source: apparent frequency increases. Formula: \(f' = f\dfrac{v+v_o}{v} = \mathbf{f(v+v_o)/v}\). (Speed of sound = \(v\), no wind.)
Q14
Standing wave \(y = 2A\sin(kx)\cos(\omega t)\). Distance between consecutive nodes:
A \(\lambda\)
B \(\lambda/2\)
C \(\lambda/4\)
D \(2\lambda\)
✅ Correct: B
Nodes occur where \(\sin(kx) = 0\) → \(kx = n\pi\) → \(x = n\pi/k = n\lambda/2\). Distance between consecutive nodes \(= \mathbf{\lambda/2}\).
Q15
Simple pendulum oscillates on Earth with \(T\). On Moon (\(g_{moon} = g/6\)), period:
A \(T/6\)
B \(\sqrt{6}\,T\)
C 6T
D \(T/\sqrt{6}\)
✅ Correct: B
\(T = 2\pi\sqrt{L/g}\). On Moon: \(T' = 2\pi\sqrt{L/(g/6)} = T\sqrt{6} = \mathbf{\sqrt{6}\,T}\).
Q16
A wave \(y = A\sin(\omega t - kx)\) has amplitude \(A\) and wavelength \(\lambda\). Phase difference between points separated by \(\lambda/3\):
A \(\pi/3\)
B \(2\pi/3\)
C \(\pi\)
D \(4\pi/3\)
✅ Correct: B
Phase difference \(\Delta\phi = k\Delta x = \dfrac{2\pi}{\lambda}\times\dfrac{\lambda}{3} = \mathbf{\dfrac{2\pi}{3}}\).
Q17
For resonance in LCR circuit, which condition holds?
A \(X_L > X_C\)
B \(X_L < X_C\)
C \(X_L = X_C\)
D \(X_L = R\)
✅ Correct: C
At resonance: \(X_L = X_C\), i.e., \(\omega L = 1/\omega C\). Impedance \(Z = R\) (minimum), current is maximum, power factor \(= 1\). \(\mathbf{X_L = X_C}\).
Q18
A particle at SHM equilibrium position has:
A Maximum PE, zero KE
B Zero PE, maximum KE
C Maximum PE and KE
D Zero PE and KE
✅ Correct: B
At equilibrium (\(x = 0\)): \(PE = \frac{1}{2}kx^2 = 0\), \(KE = \frac{1}{2}m\omega^2(A^2-x^2) = \frac{1}{2}m\omega^2A^2\) (maximum). So zero PE, maximum KE .
Q19
Beat frequency when tuning forks of 256 Hz and 260 Hz are sounded together:
✅ Correct: B
Beat frequency \(= |f_1 - f_2| = |256 - 260| = \mathbf{4\text{ Hz}}\). The ear hears 4 beats (variations in loudness) per second.
Q20
A wave has frequency 100 Hz and speed 200 m/s. Wavelength:
✅ Correct: A
\(\lambda = v/f = 200/100 = \mathbf{2\text{ m}}\). Basic relation: \(v = f\lambda\).
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Roshan
Expert · 5 Years Experience
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