A string 120cm in length sustains a standing wave with the points of the string at which the displacement amplitude is equal to 3.5mm being separated by 15 cm. Find the max. displacement amplitude.
By drawing a figure, I got wavelength as 60cm.
I took the equation of the standing wave as y = 2A*sinkx*coswt so that at t=0 ,x=7.5 and y=0.35
now y =2Asinkx
0.35=2Asin(2pi/60 * 7.5)
0.35=2A(1/√2)
A=0.25cm which is absurd value as A<0.35cm
Please help.
23max amplitude of the resultant standing wave will be 2A and not A ,
A is the amp of the waves that interfered to giv this standing wave
btw how did u find wavelength ?
1Lol...you are replying after so long
I got the answer anyways.
Hmm wavelength....nice question.
look, the distance between two points is given as 15cm.
Draw a figure with two waves.
take 3 vertical lines with amplitude 3.5mm (there are total 4 actually - take first 3)
The distance between 2nd and 3rd line is 15cm. Half of it will give the distance between 2nd line and the node- whicch is 7.5cm.
Now the distance between first and second line is 15cm again. So half of wavelength is 15 + 7.5*2 = 30cm
Total wavelength is 60cm.
23arey but why 2 waves ? i m not getting how did u decide wich harmonic frequency it is ????
1arey why do you want to know which frequenccy....woh toh baad ki baat.....
you need 2 waves to just understand and derive what is wavelength.....wich harmonic frequency it is doesnot matter......
23arey if it is fundamental frequency then 2λ =L
if it is first harmonic then λ = L
if it is nth harmonic then λ = nL /2
ur lambda very much depends on it
1mere bhai......string ki length dekho.....120cm....aur 2 displacements of string are 15cm apart......toh aise bohot sare waves honge (greater than 2 waves offcourse).
So just take 2 waves first....then find wavelength.....phir kitne harmonics hain woh toh is formulae se
λ = nL /2
I think you did not understand how I am finding wavelength....I am NOT using this formula for finding wavelength....just by drawing figure with 2 waves and finding out logically.
23oh okk okk got it !! nicely done !
never thought it dat way ... sorry for wasting ur time though [4] !!!
