Home
Class 11
PHYSICS
The transverse displacement of a string ...

The transverse displacement of a string (clamped at its both ends) is given by
`y(x, t) = 0.06 sin ((2 x)/(3) x) cos (120 pi t)`
where x and y are in m and t in s. The length of the string is 1.5 m and its mass is `3.0 xx 10^(-2) kg`.
Answer the following :
(a) Does the function represent a travelling wave or a stationary wave?
(b) Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength, frequency , and speed of each wave ?
(c ) Determine the tension in the string.

Text Solution

Verified by Experts

(a) Stationary wave (b) `l=3, n=60Hz, and v= 180 ms^(-1)` for each wave
(c ) 648N
Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

The transverse displacement of a string is given by y ( x , t ) = 0.06 sin ((2pi)/(3)) x cos ( 120 pi t) where 'x' & 'y' are 'm' and 't' is s. The length of the string is 1.5m and its mass is 3.0 xx 10^(-2) kg . Determine the tension in the string.

The transverse displacement of a string is given by y ( x , t ) = 0.06 sin ((2pi)/(3)) x cos ( 120 pi t) where 'x' & 'y' are 'm' and 't' is s. The length of the string is 1.5m and its mass is 3.0 xx 10^(-2) kg . Does the function represent a travelling wave or stationary wave ?

Knowledge Check

  • A wave is given by the equation Y = 10^(-4) sin (60t + 2x) where x and y are in metres and t in second, then wavelength of the wave is :

    A
    `pi` metre
    B
    `2pi` metre
    C
    `(3pi)/(2)` metre
    D
    `3pi` metre

  • The wave described by y = 0.25 sin (10 pi x - 2 pi t ) where x and y are in metres and t in seconds, is a wave travelling along the :

    A
    `+` ve x -direction with frequency `pi` Hz and wavelength `lambda` = 0.2 m.
    B
    `+` ve x-direction with frequency 1 Hz and wavelength `lambda` = 0.2 m.
    C
    `-`ve x-direction with amplitude 0.25 m and wavelength `lambda` = 0.2 m
    D
    `-`ve x -direction with frequency 1 Hz.

  • The transverse displacement y(x,t) of a wave on a string is given by y (x,t) = e^(-(ax^(2) + bt^(2) + 2 sqrt("abxt"))) . This represents a :

    A
    wave moving in -x direction with speed `sqrt((b)/(a))`
    B
    Standing wave of frequency `sqrt(b)`
    C
    Standing wave of frequency `(1)/(sqrt(b))`
    D
    wave moving in + x direction with speed `sqrt((a)/(b))`

    • Similar Questions

    Explore conceptually related problems

    The transverse displacement of a string is given by y ( x , t ) = 0.06 sin ((2pi)/(3)) x cos ( 120 pi t) where 'x' & 'y' are 'm' and 't' is s. The length of the string is 1.5m and its mass is 3.0 xx 10^(-2) kg . Interpret the wave as a superposition of two waves travelling in opposite direction. What is the wavelength, frequency and speed of each wave?

    The equation of a transverse wave is given by y=20sinpi(0.02x-2t) where y and x are in cm and t is in sec. The wavelength in cm will be

    A stationary wave on a stretched string has an equation given by y = 10 sin (2pi x)/(3) cos 8 pi t, where x and y are in cm and t is in second. Then separation between the two adjacent nodes is given by :

    The equation of a simple harmonic wave is given by y=5 "sin"(pi)/(2)(100 t-x) where x and y are in metre and time is in second. The period of the wave in second will be

    The equation of a transverse travelling wave on a string is y = 2 cos pi (0.5xx - 200t) , where x and y are in cm and r in sec. Then the velocity of propagation of the wave is

    Home
    Profile