Home
Class 11
PHYSICS
The equation for a wave travelling in x-...

The equation for a wave travelling in x-direction on a string is y =(3.0cm)sin[(3.14 cm^(-1) x - (314s^(-1))t]` (a) Find the maximum velocity of a particle of the string. (b) Find the acceleration of a particle at x =6.0 cm at time t = 0.11 s.

Text Solution

AI Generated Solution

To solve the problem, we will break it down into two parts: (a) finding the maximum velocity of a particle of the string and (b) finding the acceleration of a particle at a specific position and time. ### Part (a): Finding the Maximum Velocity 1. **Identify the wave equation**: The wave equation is given as: \[ y = (3.0 \, \text{cm}) \sin\left(3.14 \, \text{cm}^{-1} \, x - (314 \, \text{s}^{-1}) \, t\right) ...
Promotional Banner

Topper's Solved these Questions

  • WAVE MOTION AND WAVES ON A STRING

    HC VERMA|Exercise Short Answer|7 Videos

  • WAVE MOTION AND WAVES ON A STRING

    HC VERMA|Exercise Objective 1|22 Videos

  • WAVE MOTION AND WAVES ON A STRING

    HC VERMA|Exercise Exercises|57 Videos

  • THE FORCES

    HC VERMA|Exercise Exercises|12 Videos

  • WORK AND ENERGY

    HC VERMA|Exercise Exercises|64 Videos

Similar Questions

Explore conceptually related problems

The equation for a wave travelling in x-direction 0n a string is y = (3.0 cm) sin [(3.14 cm^(-1) x -(314 s^(-1)t] (a) Find the maximum velocity of a particle of the string. (b) Find the acceleration of a particle at x = 6.0 cm at time t = 0.11 s

The equation for a wave travelling in x-direction on a string is : y = (3 cm) sin [(pi cm^(-1)) x - (314)s^(-1)t] Then find acceleration of a particle at x = 6 cm at t = 0.11 sec-

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?

The equation of a standing wave, produced on a string fixed at both ends, is y = (0.4 cm) sin[(0.314 cm^-1) x] cos[(600pis^-1)t] What could be the smallest length of the string ?

The equation of a wave travelling on a string is y=(0.10mm)sin[3.14m^-1)x+(314s^-1)t] . (a) In which direction does the wave 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 ?

Two waves passing through a region are represented by y=(1.0cm) sin [(3.14 cm^(-1))x - (157s^(-1) x - (157s^(-1))t] and y = (1.5 cm) sin [(1.57 cm^(-1))x- (314 s^(-1))t]. Find the displacement of the particle at x = 4.5 cm at time t = 5.0 ms.

The equetion of a progressive wave travelling along a string is given by y=10 sinpi(0.01x-2.00t) where x and y are in centimetres and t in seconds. Find the (a) velocity of a particle at x=2 m and t=5//6 s. (b) acceleration of a particle at x=1 m and t=1//4 s. also find the velocity amplitude and acceleration amplitude for the wave.

The equation of a standing wave, set up in a string is, y=0.8 sin[(0.314 cm^(-1) )x]cos[(1200 pis^(-1) )t]. Calculate the smallest possible length of the living.

The eqyation of wave is x= 5sin ((t)/( 0.4) -( x)/(4))cm the maximum velocity of the particles of the medium is

A travelling wave is produced on a long horizontal string by vibrating an end up and down sinusoidal. The amplitude of vibration is 1.0cm and the displacement becomes zero 200 times per second. The linear mass density of the string is 0.10 kg m^(-1) and it is kept under a tension of 90 N. (a) Find the speed and the wavelength of the wave. (b) Assume that the wave moves in the positive x-direction and at t = 0 the end x= 0 is at its positive extreme position. Write the wave equation. (c ) Find the velocity and acceleration of the particle at x = 50 cm at time t = 10ms.