Home
Class 11
PHYSICS
The displacement of an elastic wave is g...

The displacement of an elastic wave is given by the function `y=3 sin omega t +4 cos omegat .`
where y is in cm and t is in second. Calculate the resultant amplitude.

Text Solution

Verified by Experts

Given , displacement fo an elastic wave `y=3sinomegat+4cosomegat,`
Assume, `" " 3=acosphi " " ...(i)`
`" " 4=a sinphi" " ...(ii)`
On divinding Eq. (ii) by Eq. (i)
`" " tanphi=(4)/(3)rArrphi=tan^(-1)(4//3)`
Aslo `" " a^(2)cos^(2)phi+a^(2)sin^(2)phi=3^(2)+4^(2)`
`rArr " " a^(2)(cos^(2)phi+sin^(2)phi)=25`
Hence, `" " y=5cosphisinomegat+5sinhphicosomegat`
`" " =5[cos phisin omegat + sin phi cos omegat]=5sin(omegat+phi)`
where `" " phitan^(-1)(4//3)`
Hecne, amplitude =5 cm
Promotional Banner

Topper's Solved these Questions

  • WAVES

    NCERT EXEMPLAR|Exercise SHORT ANSWER TYPE QUESTIONS|7 Videos

  • WAVES

    NCERT EXEMPLAR|Exercise LONG ANSWER TYPE QUESTIONS|5 Videos

  • WAVES

    NCERT EXEMPLAR|Exercise MULTIPLE CHOICE QUESTIONS (MORE THAN ONE OPTIONS )|7 Videos

  • UNITS AND MEASUREMENTS

    NCERT EXEMPLAR|Exercise Long Answer Type Questions|9 Videos

  • WORK, ENERGY AND POWER

    NCERT EXEMPLAR|Exercise Long answer|1 Videos

Similar Questions

Explore conceptually related problems

The displacement of an eleastic wave is given by the function y=3 sin omega t +4 cos omegat . where y is in cm and t is in second. Calculate the resultant amplitude.

The S.H.M. of a particle is given by the equation y=3 sin omegat + 4 cosomega t . The amplitude is

The displacement of an oscillator is given by x=a sin omega t+b cos omega t where a, b and omega , are constant. Then -

Two waves are represented by the equations y_1=a sin omega t and y_2=a cos omegat . The first wave

The equation of a plane progressive wave is give by equation y=10sin2pi(t-0.005x) where y and x are in cm and t is in seconds. Calculate the amplitude, frequency, wavelength and velcoity of the wave.

The displacement of a standing wave on a string is given by y (x,t) = 0.4 sin (0.5x) cos (30t) where x and y are in centimetres. (a) Find the frequency, amplitude and wave speed of the component waves. (b) What is the particle velocity at x=2.4 cm at t=0.8 s ?

The displacement of a particle of a string carrying a travelling wave is given by y = (3 cm) sin 6.28 (0.50 x – 50 t) where x is in centimeter and t is in second. The velocity of the wave is-

The displacement of a progressive wave is represented by y = A sin (omegat - kx), where x is distance and t is time. Write the dimensional formula of (i) omega and (ii) k.

The equation of displacement of a harmonic oscillator is x = 3sin omega t +4 cos omega t amplitude is