Home
Class 11
PHYSICS
Equation of a transverse wave travelling...

Equation of a transverse wave travelling in a rope is given by
`y=5sin(4.0t-0.02 x)`
where y and x are expressed in cm and time in seconds. Calculate
(a) the amplitude, frequency,velocity and wavelength of the wave.
(b) the maximum transverse speed and acceleration of a particle in the rope.

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
(a) Comparing this with the standard equation of wave motion,
`y=Asin(omegat-kx)=Asin(2pift-(2pi)/(lambda)x)`
where A, f and lambda are amplitude, frequency and wavelength respectively.
Thus, amplitude `A=5cm`
`rArr 2pif=4 rArr "Frequency", `f=(4)/(2pi)=0.637 Hz`
Again `(2pi)/(lambda)=0.02` or Wavelength, `lambda=(2pi)/(0.02)=(100pi)cm`
Velocity of the wave, `v=flambda=(4)/(2pi)(2pi)/(0.02)=200cm//s`
(b) Transverse velocity of the particle,
`v_p=(dely)/(delt)=5xx4cos(4.0t-0.02x)=20cos(4.0t -0.02x)`
Maximum velocity of the particle `=20cm//s`
Particle acceleration, `a_p=(del^2y)/(delt^2)=-20xx4sin(4.0t-0.02x)`
Maximum particle acceleration `= 80cm//s^2`
Promotional Banner

Topper's Solved these Questions

  • WAVE MOTION

    DC PANDEY ENGLISH|Exercise Example Type 1|1 Videos

  • WAVE MOTION

    DC PANDEY ENGLISH|Exercise Example Type 2|1 Videos

  • VECTORS

    DC PANDEY ENGLISH|Exercise Medical enrances gallery|9 Videos

  • WORK, ENERGY & POWER

    DC PANDEY ENGLISH|Exercise Level 2 Comprehension Based|2 Videos

Similar Questions

Explore conceptually related problems

The equation of a transverse wave travelling along x-axis is given by y = 10 sin pi= (0.01 x- 2.0t) where y and x are represented in centimeters and, in seconds. Find the amplitude, frequency velocity and wavelength of the wave.

The equation of a transverse wave travelling along +x axis is given by y=0.15 sin (1.57x-31.4t) where y and x are represented in m and t in s. Find the amplitude, frequency velocity and wavelength of the wave.

The equation of a progressive wave is y= 1.5sin(328t-1.27x) . Where y and x are in cm and t is in second. Calcualte the amplitude, frequency, time period and wavelength of the wave.

The equation of a transverse wave travelling in a rope is given by y=7 sin (4.0 t-0.02 x) where y and x are in cm and the time is in second. Calculate (i) the maximum transverse speed and (ii) the maximum particle acceleration?

The equation of a wave travelling in a rope is given by y=10 sin (2.0 t-0.04x) where y and x are expressed in cm and time t in second. Calculate the intensity of the wave if the density of the material of the rope is 1.3 xx 10^(3)kg//cm^3 .

The equation of progressive wave is given by y=10sin[300pi(t-(x)/(480))] where x and y are in metre and t is in second. Calculate the amplitude frequency time period and wavelength of the wave.

The equation of a transverse wave travelling on a rope given by y=10sinpi(0.01x-2.00t) whrer y and x are in cm and t in second .This maximum traverse speed of a particle in the rope is about

A transverse wave travelling on a taut string is represented by: Y=0.01 sin 2 pi(10t-x) Y and x are in meters and t in seconds. Then,

The equation of a progressive wave is given by y=a sin (628 t-31.4 x) If the distances are expressed in cms and time in seconds, then the wave velocity will be

The equation for the transverse wave travelling along a string is y = 4 sin 2pi ((t)/(0.05) -(x)/(60)) lengths expressed in cm and time period in sec. Calculate the wave velocity and maximum particle velocity.