A wave pulse is traveling on a string with a speed v towards the positive x -axis. The shape of the string at t = 0 is given by y ( x ) = A sin x a where, A and a are constants. (a) What are the dimensions of A and a ? (b) Write the equation of the wave for a general time t if the wave speed is v .

(a) From the given equation at t = 0 , y = A sin x a . . . 1 From dimension analysis, → The dimension of the left-hand side is equal to right-hand side. → All trigonometric functions are dimensionless. From equation 1 , dimension of A is equal to dimension of y which is M 0 L T 0 . dimension of a is equal to dimension of x which is M 0 L T 0 . (b) As the wave is travelling in positive x -direction, there should be a negative sign between the term of x and term of t . The general equation is given by, y = A sin α x - β t . . . 2 α = coefficient of x , β = coefficient of t . From formula, speed of wave = coefficient of t coefficient of x . . . 3 Comparing equations 1 and 2 , α = 1 a . From equation 3 , v = β α = a β β = v a . Putting above values in equation 2 , y = A sin x - v t a .

A wave pulse is traveling on a string with a speed v towards the positive x -axis. The shape of the string at t = 0 is given by y ( x ) = A sin x a where, A and a are constants. (a) What are the dimensions of A and a ? (b) Write the equation of the wave for a general time t if the wave speed is v .

(a) From the given equation at t = 0 , y = A sin x a . . . 1 From dimension analysis, → The dimension of the left-hand side is equal to right-hand side. → All trigonometric functions are dimensionless. From equation 1 , dimension of A is equal to dimension of y which is M 0 L T 0 . dimension of a is equal to dimension of x which is M 0 L T 0 . (b) As the wave is travelling in positive x -direction, there should be a negative sign between the term of x and term of t . The general equation is given by, y = A sin α x - β t . . . 2 α = coefficient of x , β = coefficient of t . From formula, speed of wave = coefficient of t coefficient of x . . . 3 Comparing equations 1 and 2 , α = 1 a . From equation 3 , v = β α = a β β = v a . Putting above values in equation 2 , y = A sin x - v t a .

E M B I B E

Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 1 - Wave Motion>Exercises>Q 4

HARD

JEE Advanced

IMPORTANT

Earn 100

A wave pulse is traveling on a string with a speed $v$ towards the positive $x$ -axis. The shape of the string at $t = 0$ is given by $y (x) = A \sin (\frac{x}{a})$ where, $A$ and $a$ are constants.
(a) What are the dimensions of $A$ and $a$ ?
(b) Write the equation of the wave for a general time $t$ if the wave speed is $v$ .

Important Questions on Wave Motion

MEDIUM

JEE Advanced

IMPORTANT

Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 1 - Wave Motion>Exercises>Q 5

Figure shows a plot of the transverse displacement of the particle of a string at $t = 0$ through which a traveling wave is passing in the positive $x$ -direction. The wave speed is $20 cm s^{- 1}$ . Find (a) the amplitude (b) the wavelength (c) the wave number and (d) the frequency of the wave.

Question Image

MEDIUM

JEE Advanced

IMPORTANT

Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 1 - Wave Motion>Exercises>Q 6

Two wires of different densities but same area of cross-section are soldered together at one end and are stretched to tension

T

. The velocity of a transverse wave in the first wire is double of that in the second wire. Find the ratio of the density of the first wire to that of the second wire.

HARD

JEE Advanced

IMPORTANT

Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 1 - Wave Motion>Exercises>Q 7

Two long strings

A

and

B

, each having linear mass density

1.2 \times 10^{- 2} kg m^{- 1}

, are stretched by different tensions

4.8 N

and

7.5 N

, respectively, and are kept parallel to each other with their left ends at

x = 0

. Wave pulses are produced on the strings at the left ends at

t = 0

on string

A

and at

t = 20 ms

on string

B

. When and where will the pulse on

B

overtake that on

A

.

HARD

JEE Advanced

IMPORTANT

Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 1 - Wave Motion>Exercises>Q 8

A sinusoidal transverse wave travels on a string. The string has length $8.00 m$ and mass $6.00 g$ . The wave speed is $30.0 m s^{- 1}$ and the wavelength is $0.200 m$ .

(a) If the wave is to have an average power of $50.0 W$ , what must be the amplitude of the wave?

(b) For this same string, if the amplitude and wavelength are the same as in part (a) what is the average power for the wave if the tension is increased such that the wave speed is doubled?

HARD

JEE Advanced

IMPORTANT

Understanding Physics JEE Main & Advanced WAVES AND THERMODYNAMICS>Chapter 1 - Wave Motion>Exercises>Q 9

A uniform rope, with length