00:01
The equation of a standing wave is given by y of x d is equal to 2a sine k x force omega d.
00:13
Here 2a is the maximum amplitude, k is the wave vector and omega is the angular frequency.
00:20
The time part does not play any role in the amplitude of the motion.
00:26
Therefore, the amplitude of the standing wave is given by a f, a of x is equal to 2a sine k the equation for the wave vector is given by k is equal to 2 pi by lambda here lambda is the wavelength the equation for the wavelength of the nth harmonic is given by lambda n is equal to 2 l by n here the value of n is equal to 2 therefore the value of wavelength wave becomes lambda 2 is equal to 2 l by 2 or lambda 2 is equal to l therefore the way vector becomes k is equal to 2 pi by l.
01:09
Substituting thus in the equation for the amplitude gives a of x is equal to 2a sign 2 pi by l into x it is given that the value of 2a is 2 .0 centimeter substituting this in the equation gives a of x is equal to 2 .0 centimeter into sine 2 pi by 2 .0 meter into x or converting to essay unit scales a of x is equal to 2 .0 centimeter into 1 meter divided by 100 centimeter into sine pi x or or a of x is equal to 0 .02 sine pi x.
02:10
The amplitude of the most oscillation when x is equal to 10 centimeter is found as a of 10 centimeter is equal to 0 .02 sine pi into 10 centimeter.
02:24
Converted to meters, case a of 10 centimeter is equal to 0 .02 sine into sine by into 10 cm into 1 meter divided by 100 cm which is equal to 6 .18 into 10 raise to minus 3 meter.
02:46
Therefore, the amplitude of the most oscillation at x is equal to 10 centimeter is 6 .18 into 10 to minus 3 meter...