Home
Class 12
PHYSICS
The equation of a standing wave produced...

The equation of a standing wave produced on a string fixed at both ends is `y=0.4 "sin"(pix)/(10) cos 600 pi t` where y' is measured in om 10 What could be the smallest length of string?

Text Solution

AI Generated Solution

To find the smallest length of the string that can produce a standing wave given the equation \( y = 0.4 \sin\left(\frac{\pi x}{10}\right) \cos(600 \pi t) \), we can follow these steps: ### Step 1: Identify the wave number \( k \) The given equation can be compared to the general form of a standing wave: \[ y = 2a \sin(kx) \cos(\omega t) \] From the given equation, we can see that: \[ k = \frac{\pi}{10} \] ...
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

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 wave-function for a certain standing wave on a string fixed at both ends is y(x,t) = 0.5 sin (0.025pix) cos500t where x and y are in centimeters and t is seconds. The shortest possible length of the string is :

The equation of a standing wave in a string fixed at both its ends is given as y=2A sin kx cos omegat . The amplitude and frequency of a particle vibrating at the point of string midway between a node and an antinode is

The equation of a transverse wave travelling along a string is given by y=0.4sin[pi(0.5x-200t)] where y and x are measured in cm and t in seconds. Suppose that you clamp the string at two points L cm apart and you observe a standing wave of the same wavelength as above transverse wave. For what values of L less than 10 cm is this possible?

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

The transvers displacement of a string (clamped at its both ends) is given by y(x,t) = 0.06 sin ((2pi)/(3)s) cos (120 pit) Where x and y are in m and t in s . The length of the string 1.5 m and its mass is 3.0 xx 10^(-2) kg . Answer the following : (a) Does the funcation represent a travelling wave or a stational wave ? (b) Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength. Frequency and speed of each wave ? Datermine the tension in the string.

The vibrations of a string fixed at both ends are represented by y = 16 sin (pi x/15) cos 96 pi t where x and y are in cm and t in seconds. Then the phase difference between the points at x = 13 cm and X = 16 cm in radian is

The equation of a wave distrubance is a given as y= 0.02 sin ((pi)/(2)+50pi t) cos (10 pix) , where x and y are in metre and t is in second . Choose the correct statement (s).

The transverse displacement of a string clamped at its both ends is given by y(x, t) = 0.06 sin ((2pi)/3 x) cos(l20pit) where x and y are in m and t in s. The length of the string is 1.5 m and its mass is 3 xx 10^(-2) kg. The tension in the string is

The equation of a wave travelling in a string can be written as y = 3 cos pi (10t-x) . Its wavelength is