Wave Equation

Q.

Two tuning forks of frequencies 256 and 258 vibrations/sec are sounded together, then time interval between consecutive maxima heard by the observer is

1. 2 sec

2. 0.5 sec

3. 250 sec

4. 252 sec

Q.

A body of mass 5 gm is executing S.H.M. about a point with amplitude 10 cm. Its maximum velocity is 100 cm/sec. Its velocity will be 50 cm/sec at a distance

[CPMT 1976]

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Q.

You have learnt that a travelling wave in one dimension is represented by a function y = f (x, t) where x and t must appear in the combination x – υ t or x + v t, i.e. y = f (x ± υ t). Is the converse true? Examine if the following functions for y can possibly represent a travelling wave :

(a) (x – υ t )²

(b) log [(x + υ t)/x0]

(c) 1/(x + υt)

Q. A travelling harmonic wave on a string is described by y(x, t) = 7.5 sin (0.0050x +12t + π/4) (a)what are the displacement and velocity of oscillation of a point at x = 1 cm, and t = 1 s? Is this velocity equal to the velocity of wave propagation? (b)Locate the points of the string which have the same transverse displacements and velocity as the x = 1 cm point at t = 2 s, 5 s and 11 s.

Q.

The restoring force in a simple harmonic motion is _________ in magnitude when the particle is instantaneously at rest.

1. maximum

2. minimum

3. zero

Q. A particle with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force Fsinwt . If the amplitude of the particle is maximum for w=w1 and energy of the particle is maximum for w=w2 , then (where w° is natural frequency of oscillation of particle) (a)w1=w° and w2not=w° (b)w1=w° & w2=w° (c) w1 not=w° & w2=w° (d)w1not=w° & w2 not=w°

Q. 32. The mathematical forms for three sinusoidal travelling waves are given by Wave 1:y(x, t)=(2cm) sin (3x-6t) Wave 2:y(x, t)=3cm sin (4x-12t) Wave 3:y(x, t) =4cm sin(5x-11t) Where x is in metres and t in seconds of these waves

Q. a single degree of freedom spring mass system with viscous damping has a spring constant of 10kN/m, this system is excited by a sinusoidal force of amplitude 100N. if the damping coefficient is 0.25kg/s, then find amplitude at resonance condition

Q. 202 If the period of oscillation of particle performing SHM is 8s. Then the frequency of its kinetic energy will be 1. 0.5 /s 2. 0.25 /s 3. 1 /s 4. 2 /s

Q. A police jeep moving towards a cliff sounds its horn. The driver observes that sound reflected from the cliff has a pitch one octave higher than the actualsound of horn. If v is the velocity of the soundvelocity of jeep is

Q.

Under forced oscillation, the phase of the harmonic motion of the particle and phase of driving force

1. Are same

2. Both are zero

3. Not present

4. Are different

Q. A wave pulse is traveling on a string at 2 m/s. Displacement y of the particle at x = 0 at any time t is given by $\frac{2}{(t^2+1)}$. Find the expression of the function y = (x, t), i.e., displacement of the particle at position x and time t.

1. $y=\frac{2}{{(t-\frac{x}{2})}^2+1}$
2. $y=\frac{2}{{(t-\frac{x}{4})}^2+1}$
3. $y=\frac{2}{{(t-2x)}^2+1}$
4. $y=\frac{2}{{(t-4x)}^2+1}$

Q. A wave is moving towards positive X-axis. Then the point (s) at which accelerationand velocity of particle are parallel to each other

Q.

If you blow air over the top of a fairly large drinking straw you can hear a fundamental frequency due to a standing wave being set up in the straw. What happens to the fundamental frequency if while blowing you cut the straw in half with a pair of scissors?

1. The fundamental frequency decreases

2. The fundamental frequency increases

3. The fundamental frequency remains unchanged

Q. 20. a particle executes linear SHM of period 4second and amplitude 4 cm , the time taken by it to describe a distance of 1 cm from the extreme position

Q. For the travelling harmonic wave y(x, t) = 2.0 cos 2π (10t – 0.0080 x + 0.35) where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of (a) 4 m, (b) 0.5 m, (c) λ /2, (d) 3λ /4

Q. a particle exeutes shm with amplitude a. if the time taken by the particle to travel from -A to A/2 is 4 seconds. its time period is?

Q. 40.Sound of frequency f passes through a Quincys tube, adjusted for intensity Im.What should be the length to which the tube should be moved to reduce intensity to 50%(speed of sound is v)?

Q. fundamental frequency of a open pipe is 30 Hz. if 2nd harmonic of open pipe is same as 3rd harmonic of close pipe. find length of air column in 2 pipe.(speed of sound in air =330 m/s)

Q. a particle is performing SHM of Amplitude A and time period T. then find (a) minimum time taken to travel dis†an ce A (b) also find maximum time taken by same particle to travel ds†an ce A

Q. The displacement of the particle at x=0 of a stretched string carrying a wave in the positive x -direction is given { by f(t)=A\operatorname{sin(t/T). The wave speed is v . Write the wave equation.

Q.

A wave represented by the given equation y = a cos ( kx - $\omega$ t ) is superposed

with another wave to form a stationary wave such that the point x = 0 is a

node. The equation for the other wave is

AIIMS 1998; SCRA 1998; MP PET 2001; KCET 2001;

AIEEE 2002; UPSEAT 2004]

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Q. A standard tunic fork of frequency f is use to find velocity of sound in air by resonance column apparatus.the difference between two resonating length is 1m .then the velocity of sound in air is

Q. Which of the following equations represents a wave travelling along Y-axis?
(a) $x=A\sin \left(ky-\omega t\right)$
(b) $y=A\sin \left(kx-\omega t\right)$
(c) $y=A\sin ky\cos \omega t$
(d) $y=A\cos ky\sin \omega t$.

Q.

A particle of mass m is attached to three identical springs A, B and C each of force constant k as shown in figure. If the particle of mass m is pushed slightly against the spring A and released, the time period of oscillation is:

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Q. Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal (P) sound waves. Typically the speed of S wave is about 4.0 km $s^{-1}$ and that of P wave is 8.0 km $s^{-1}$. A seismograph records P and S waves from an earthquake. The first P wave arrives 4 min before the first S wave. Assuming the waves travel in straight line, at what distance does the earthquake occur ?

Q. The displacement of the particle at x = 0 of a stretched string carrying a wave in the positive x-direction is given f(t) = A sin (t/T). The wave speed is $\nu$. Write the wave equation.

Q. The frequency changes by 10% as a sound wave approaches a stationary observer with constant speed vs . What would be percentage change n the frequency as the source recedes the observer with same speed (vs