**Oscillations and Waves** is considered as the most difficult chapters by most of the students. In many schools, these chapters are not properly discussed and taught due to the lack of time they face during the last term. Further the lack of proper explanations for the different concepts and steps in the text book also add to the toughness. So, here are some questions which you can attempt to practice. If you have doubt with answering any of these questions, ask them at www.askphysics.com

**OSCILLATIONS**

- What is a simple harmonic motion? State its characteristics.
- What will be the effect on time period, if the amplitude of a simple pendulum increases?
- Define force constant of a spring. Show that in S.H.M, the acceleration is directly proportional to its displacement at the given instant.
- Show that for a particle in linear simple harmonic motion ,the average kinetic energy over a period of oscillation, equals the average potential energy over the same period.
- At what distance from the mean position, is the K.E in simple harmonic oscillator equal to P.E ?
- A body weighing 10 Kg has a velocity of 6m/s, after one second of starting from the mean position .If the time period is 6 second, find the kinetic , potential and total energy.(180 J,720J, 540 J.)
- A body is execution S.H.M. of amplitude 1m. Its velocity while passing through the mean position is 10m/s. Find its frequency.(1.592Hz.)
- The periodic time of a body executing S.H.M, is 2 seconds . After how much interval from t =0, will its displacement be half of its amplitude ? (1/6 sec.)
- A particle executing S.H.M.along a straight line has a velocity of 4m/sec, when at a distance of 3m from its mean position and 3m/sec , when at a distance of 4m from it.Find the time it takes to travel 2.5m from the positive extremity of its oscillation.(a=5m,w=1rad/sec.)
- The shortest distance traveled by a particle executing S.H.M. from mean position in 2 seconds is equal to /2 times its amplitude .Determine its time period.

(T= 12 sec) - A particle executes S.H.M. of amplitude a. At what distance from the mean position is its kinetic energy equal to its potential energy.
- Show that for a particle in linear S.H.M. the average kinetic energy over a period of oscillation equals the average potential energy over the same period.
- A spring balance has a scale that reads 50 Kg . The length of the scale is 20 cm. A body ,suspended from this spring is when displaced and released , it oscillates with period of 0.60 s. What is the weight of the body.(22.36 Kgf).
- A spring of force constant 1200 N/m is mounted on a horizontal table .A mass of 3 Kg is attached to the free end of the spring , pulled sideways to a distance of 2cm and released .(a) What is the frequency of oscillation of the mass? (b) What is the maximum acceleration of the mass? (c) What is the maximum speed of the mass?
- The acceleration due to gravity on the surface of moon is 1.7 m/s2.What is the time period of a simple pendulum on the moon if its time period is 3.5 sec on the earth?

(8.4 sec) - A pendulum clock normally shows correct time. On an extremely cold day, its length decreases by 0.2%. Compute the error in time per day.(86.4%)
- What do you understand by Simple Harmonic Motion? Explain its geometrical interpretation.
- Explain displacement, velocity, acceleration, and time period of a simple harmonic motion. Find relation between them.
- Explain the relation in phase between displacement, velocity and acceleration in S.H.M. graphically as well as theoretically.
- Find the total energy of a particle executing S.H.M. and show graphically the variation of P.E and K.E with time in S.H.M. What is the frequency of these Energies w.r.t the frequency of the particle executing S.H.M.
- Explain the oscillation of a loaded spring and find the relations for the time period and frequency in case of (i) horizontal spring (ii) vertical spring.
- Distinguish between free, forced, and resonant oscillation with illustration.
- What is spring constant? Find its value in case of two springs connected in

(i)series, (ii) parallel.

**W A V E S**

- Why longitudinal waves are called pressure waves?
- Transverse waves are not formed in liquids and gases why?
- What is a harmonic wave function?
- We can recognize our friends by their voices .Why?
- A source of sound is moving towards a stationary observer. Is the increase in pitch due to (1) increase in velocity of sound? (2) Actual or apparent change in wavelength? (3) Both?
- What is the function of water in the resonance apparatus? Can we use any other liquid?
- Why a tuning fork has two prongs? What are the conditions for resonance of air column with a tuning fork?
- What are fundamental note and overtones? What are harmonics?
- Briefly explain the terms wavelength, frequency, time period and velocity of wave motion. Establish relation between them.
- Explain some significant properties of wave motion.
- State Newton,s formula for velocity of sound in air. Point out the error and hence discuss Laplace, s correction. Discuss the effect of temperature, pressure, and density on velocity of sound in gases.
- Obtain the equation of a plane progressive simple harmonic wave.
- Establish the relation between particle velocity and wave velocity.
- State and explain superposition of waves.
- What are stationary waves? Discuss graphical method for the formation of stationary waves on stretched strings.
- Discuss the characteristics of stationary waves.
- Audible frequencies have a range 40Hz. To 30,000 Hz. Express this range in terms of (1) period T, (2) wavelength ? in air, and (3) angular frequency, Give velocity of sound in air is 350 m/s. (2.5 x 10-2s, 3.3 x 10-5s, 8.75m, 0.012m, 80? rad/secand 60,000? rad /sec.)
- If the splash is heard 4.23 seconds after a stone is dropped into a well , 78.4m deep, find the velocity of sound in air. (340.87 m/sec)
- Find at what temperature the velocity of sound in air will be 1 times the velocity at 110C.(3660)
- The velocity of sound in air at N.T.P is 331m/s . Find its velocity when the temperature rises to 910C and its pressure is doubled.(382.1m/s)
- For the traveling harmonic wave, y = 2.0 cos2?[ 10t – 0.0080x + 0.35], where x and y are in cm. and t is in sec.What is the phase difference between oscillatory motion at two points separated by a distance of (1) 4m, (2) 0.5 m (3) ?/2 (4) 3?/4. (400cm.

?=0.8? rad. , 3?/2 rad.) - Two tuning forks when sounded together, produce 3 beats per second. On loading one of them with a little wax, 20 beats are heard per second.Find its frequency if that of other is 386 Hz. (383 Hz.)
- Calculate the velocity of sound in a gas in which two wave lengths 2.04m produce 20 beats in 6 seconds.(353.6 m/s).
- A set of 24 tuning forks is arranges in series of increasing frequencies. If each fork gives 4 beats with the preceding one and the last fork is octave of the first,
- calculate the frequency of the first , calculate the frequency of the first and the last fork. (184 Hz.)
- A string 1m long with mass 0.1gm/cm is under a tension of 400newton. Find the fundamental frequency.(100 Hz.).
- A steel rod 100cm long is clamped at the middle of it. The fundamental frequency of longitudinal vibrations of the rod is given to be 2.53 kHz. What is the speed of sound in steel(5.06 x 103m/sec.)

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