Home
Class 12
PHYSICS
A wave travelling along a string is desc...

A wave travelling along a string is described by, `y(x, t) = 0.005 "sin" (80.0 x – 3.0 t)`, in which the numerical constants are in SI units `(0.005 m, 80.0 "rad" m^(-1)`, and `3.0 "rad" s^(-1))`. Calculate (a) the amplitude, (b) the wavelength, and (c) the period and frequency of the wave. Also, calculate the displacement y of the wave at a distance x = 30.0 cm and time t = 20 s ?

Text Solution

Verified by Experts

On comparing this displacement equation
`y(x,t)= a sin (kx-omega t+phi)` we find
(a) the amplitude of the wave is 0.005 m = 5 mm
(b) the angular wave number k and angular frequency `omega are k=80.0 m^(-1)and omega=3.0 s^(-1)`
We then relate the wavelength a to k through the equation
`T=2pi// omega=(2pi)/(3.0 s^(-1))=2.09s `
and frequency .`v=1//T=0.48Hz`
This displacement y at x=30.0 cm and time t-20s is given by
`y=(0.005m) sin (80.0xx0.3-3.0xx20)`
`=(0.005m)sin(-36+12pi)`
`=(0.005m) sin(97^(@))-=5mm`
Promotional Banner

Topper's Solved these Questions

  • WAVES

    AAKASH SERIES|Exercise EXERCISE-IA (Theoretical questions :)|85 Videos

  • WAVES

    AAKASH SERIES|Exercise EXERCISE-IA (Statement type questions:)|18 Videos

  • WAVE OPTICS

    AAKASH SERIES|Exercise PROBLEMS (LEVEL - II)|33 Videos

  • WAVES OPTICS

    AAKASH SERIES|Exercise EXERCISE -III (POLARISITION)|10 Videos

Similar Questions

Explore conceptually related problems

A wave travelling along a strong is described by y(x,t)=0.005 sin (80.0x-3.0t) in which the numerical constants are in SI units (0.005m, 80.0 rad m^(-1) and 3.0 rad s^( -1)) . Calculate (a) the amplitude. (b) the wavelength (c) the period and frequency of the wave. Also , calculate the displacement y of the wave at a distance x=30.0 cm and time t=20 s?

A wave travelling along the x-axis is described by the equation y (x, t) = 0.005 sin ( alphax - betat ). If the wavelength and time period of the wave are 0.08 m and 2 s respectively, then alpha, beta in appropriate units are

A wave travelling along the x-axis is described by the equation y (x, t) = 0.005 sin ( alphax - betat ). If the wavelength and time period of the wave are 0.08 m and 2 s respectively, then alpha, beta in appropriate units are

A wave travelling along the x-axis is described by the equation v(x, t) = 0.005 cos(alpha x - betat) . If the wavelength and the time period of the wave are 0.08m and 2.0s , respectively, then alpha and beta in appropriate units are

The displacement of a particle of a string carrying a travelling wave is given by y = (3.0cm) sin 6.28 (0.50x - 50t), where x is in centimetre and t in second Find (a) the amplitude, (b) the wavelength, (c ) the frequency and (d) the speed of the wave.

The equation of a wave travelling on a string is y = (0.10 mm) sin [(31.4 m^(-1)) x + (314 s^(-1))t] (a) In which direction does the travel? (b) Find the wave speed, the wavelength and the frequency of the wave. ( c ) What is the maximum displacement and the maximum speed of a portion of the string?

Figure shows a plot of the transverse displacements of the particles of a string at t = 0 through which a travelling wave is passing in the positive x-direction. The wave speed is 20 cms^-1 . Find (a) the amplitude, (b) the wavelength, (c) the wave number and (d) the frequency of the wave. .

A wave pulse of frequency 200 Hz, on a string moves a distance 8 m in 0.05 s. Calculate the wavelength of wave on string.

The equation of a travelling wave on a string is y = (0.10 mm ) sin [31.4 m^(-1) x + (314s^(-1)) t]

A wave travelling along the x-axis is described by the equation y(x,t) = 0.005cos (alpha x - beta t) . If the 1wavelength and the time period of the wave are 0.08m and 2.0s, respectively, then alpha/beta = n xx 5 , then the value of n is____(where alpha, beta are in appropriate units).