# PHYSICS SUGGESTION OF WAVE MOTION FOR IIT JEE PDF

## PHYSICS SUGGESTION FOR JEE ADVANCED/IIT JEE

#### WAVE MOTION

**Hello students I am Bijoy, completed B.tech from Jadavpur University and this is my educational wesite for Board Exams and JEE. Today I will give you a question set on Wave Motion for IIT JEE, this question set only made for IIT JEE level.**

Question starts from here:

Q. y ( x, t ) = \( \frac {0.8}{[(4x+5t)^2+5]} \) represents a moving pulse where x and y are in metre and t in second. Then choose the correct alternatives.

(a) Pulse is moving in positive x – direction

(b) in 2sec it will travel a distance of 2.5 m

(c) it is maximum displacement is 0.16 m

(d) it is a symmetric pulse

# One end of 12.0 m long rubber tube with a total mass of 0.9 kg is fastened to a fixed support. A cord attached to the other and passes over a pulley and supports an object with a mass of 5.0 kg. The tube is struck a transverse blow at one end. Find the time required for the pulse to reach the other end. ( g = 9.8 m/s ^{2}).

# A uniform rope of mass 0.10kg and length 2.45 m hangs from a ceiling.

(a) Find the speed of transverse wave in the rope at a point 0.5 m distant from the lower end.

(b) Calculate the time taken by a transverse wave to travel the full length of the rope.

# A stretched string is forced to transmit transverse waves by a means of an oscillator coupled to one end. The string has a diameter of 4 mm. The amplitude of the oscillation is 10^{-4} m and the frequency is 10 Hz. Tension in the string is 100 N and mass density of wire is 4.2 ×10^{3} kg/m ^{3}. Find :

(a) The equation of the waves along the string

(b) The energy per unit volume of the wave

(c) The average energy flow per unit time across any section of the string and

(d) Power required to drive the oscillator.

# A simple harmonic wave of amplitude 8 units travels along positive x – axis. At any given instant of time, for a particle at a distance of 10 cm from the origin, the displacement is +6 units, and for a particle at a distance of 25 cm from the origin, the displacement is +4 units, calculate the wavelength of the given harmonic wave.

# Wave passing through a certain medium have a dispersion relation ω (k) = ( ω_{0}^{2} + α^{2}k^{2} )^{1/2}. Here ω_{0} and α are constants. Find phase velocity and group velocity in this medium.

# Consider a wave propagating in the negative x – direction whose frequency is 100 hz. At t = 5 s the displacement associated with the wave is given by, y = 0.5 cos (0.1x). Where x and y are measured in centimeters and t in seconds. Obtain the displacement (as a functioned of x ) at t =10 s. What is the wavelength and velocity associated with the wave?

# A thin string is held at one end and oscillates vertically so that, y(x=0, t) = 8sin 4t (cm). Neglect the gravitational force. The string’s linear mass density is 0.2 kg/m and its tension is 1 N. The string passes through a bath filled with 1 kg water. Due to friction heat is transferred to the bath. The heat transfer efficiency is 50%. Calculate how much time passes before the temperature of the bath rises one degree Kelvin.

# (a) Write the expression for y as a function of x and t for a sinusoidal wave travelling along a rope in the negative x direction with the following characteristics :

A =8.0 cm, wavelength (lamda) = 80.0 cm, f = 3.00 Hz, and y (0, t) = 0 at t = 0

(b) Write the expression for y as function of x and for the wave in part (a), assuming that y (x, 0) = 0 at the point x = 10.0 cm.

# A string of length L consists of two sections : The left half has mass per unit length μ = μ_{0}/2 , whereas the right half has a mass per unit length μ^{‘} = 3μ = 3μ_{0}/2. Tension in the string is T0. Notice from the data given that this string ha same total mass as a uniform string of length L and of mass per unit length μ_{0}.

(a) Find the speeds v and v’ at which transverse wave pulses travel in the two sections. Express the speeds in term of T_{0} and μ_{0 } and also as multiplies of the speed μ_{0} = [T_{0} / μ_{0}]^{1/2}.

(b) Find the time required for a pulse to travel from one end of the string to the other. Give your results as a multiple of t_{0} = [L/v_{0}].

# A block of mass is attached with a string of mass m and length l as shown in figure. The whole system is placed on a planet whose mass and radius is three times the mass and radius of earth. Find

(a) The time taken by a wave pulse to travel from one end A to B of the string.

(b) The ratio of maximum and minimum velocity of wave pulse (g = acceleration due to gravity on earth).

# One end of each two identical springs, each of force – constant 0.5 N/m, are attached on the opposite sides of a wooden block of mass 0.1 kg. The other ends of the springs are connected to separate rigid supports such that the springs are unstitched and are collinear in a horizontal plane. To the wooden piece is fixed a pointer which touches a vertically moving plane paper. The wooden piece, kept on a smooth horizontal table is now displaced by 0.02 m along the line of spring and released. If the speed of paper is 0.1 m/s, find the equation of the path traced by the pointer on the paper and the distance between two consecutive maxima on this path.

# A long string having a cross – sectional area 0.08 mm^{2} and density 12.5 kg/m ^{3}, is subjected to a tension of 64 N along the x – axis. One end of this string is attached to vibrator moving in transverse direction at a frequency of 20 Hz. At t = 0, the source is at a maximum displacement y = 1.0 cm.

(a) Find the speed of the wave traveling on the string.

(b) Write the equation for the wave.

(c) What is the displacement of the particle of the string at x = 50 cm at time t = 0.05?

(d) What is the velocity of this particle at this instant?

Note : Answer of this part will be coming soon.

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