Oscillations and Waves
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See all →- Two identical point masses P and Q, suspended from two separate massless springs of spring constants k_1 and k_2, respectively, oscillate vertically. If their maximum speeds are the same, the ratio (A_Q/A_P) of the amplitude A_Q of mass Q to the ampl… Answer: 4. √(k₁/k₂) Key idea: the maximum speed in SHM is v_max=Aω=A√(k/m) . Masses are identical and v_max is the same, so A_P√(k₁)=A_Q√(k₂... 1
- A pipe open at both ends has a fundamental frequency f in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to : Answer: 2. f Key idea: an open pipe of length L has fundamental f=v/2L ; a pipe closed at one end of length l has fundamental v/4l . Dipping... 1
- In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency ω(t) and average amplitude A(t) of the system change with time t.… Answer: 2. Graph pair: ω(t) rises and saturates; A(t) decays Key idea: the frequency of a spring-mass system is ω=√(k/m) , and sand leaking... 1
- If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is x/2 times its original time period. Then the value of x is: Answer: 3. sqrt2 Key idea: T=2π√(L/g) does not depend on the mass of the bob. Only the length changes: T'=2π√(L/2/g)=T/sqrt2 . Setting T/sqr... 1
- If x=5≤ft(π t+π/3)m represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are : Answer: 3. 5 m, 2 s Key idea: Compare with the standard SHM form x=Asin(ω t+φ) . Here A=5 m and ω=π rad/s. Time period T=2π/ω=2π/π=2 s. Ampl... 1
- The x-t graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at t=2 s is : Answer: 1. -π²/16 mathrmm s⁻² From the graph, the amplitude is A=1 m and the particle is at the maximum at t=2 s, with a zero crossing at 4... 1