Home
Class 11
PHYSICS
The equation for the vibration of a stri...

The equation for the vibration of a string, fixed at both ends vibrating in its third harmonic, is given by ` y = (0.4 cm) sin[(0.314 cm^-1) x] cos[f(600pis^-1)t]`.(a) What is the frequency of vibration ? (b) What are the positions of the nodes ? (c) What is the length of the string ? (d) What is the wavelength and the speed of two travelling waves that can interfere to give this vibration ?

Text Solution

Verified by Experts

The correct Answer is:
a) 300Hz b) 0, 10, 20, 30 c) 30cm d) 60m/sec
the stationary wave equation is givne by
`y=(0.4cm)sin[(0.314cm^-1)x]cos[(6.00pis^-1)t]`
a. `omega=600pi`
`rarr 2pif=600pi`
`gt f=300Hz`
Wavelength
`lamda=(2pi)/0.314=((2xxx3.14))/0.314`
`=20cm`
b. therefoe Nodes are located at 0, 10 cm, 20cm, 30cm.
c. Length of the string
`=(3lamda)/a=(3xx200/2=30cm`
d. `y=0.4sin(0.314x)cos(600pit)`
`=0.4sin{(pi/10)x}cos(600pit)`
Since `lamda` and `v` are the wavelength and velocity of the wave of that interfere to give this vibration.
`lamda=20cm`
`v=omega/k=(600pi)/((pi/10))`
=6000cm/sec=60m/s`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • WAVE MOTION AND WAVES ON A STRING

    HC VERMA|Exercise Objective -2|8 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 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 ?

What are vibrations?

The frequency of vibration of a string depends on, (i) tension in the string (ii) mass per unit length of string, (iii) vibrating length of the string. Establish dimension the relation for frequency.

The frequency of vibration of string depends on the length L between the nodes, the tension F in the string and its mass per unit length m. Guess the expression for its frequency from dimensional analysis.

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 ?

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.

A stretched string is vibrating in the second overtone, then the number of nodes and antinodes between the ends of the string are respectively:

What will be the frequency sound having 0.20 m as its wavelength, when it travels with a speed of 331ms^(-1) ?

Three resonant frequencies of a string are 90, 150 and 210 Hz. (a) Find the highest possible fundamental frequency of vibration of this string. (b) Which harmonics of the fundamental are the given frequencies ? (c) Which overtones are these frequencies ? (d) If the length of the string is 80 cm, what would be the speed of a transverse wave on this string ?

If the thickness of a vibrating string is increased, its pitch ____.?

Home
Profile