Question

The equation of a stationary wave in a string is Y = 4 mm sin [(3.14m^-1)x] cos wt. Select the correct alternatives:a) The amplitude of component waves is 2mm.
b) The amplitude of component waves is 4mm.
c) The smallest possible string is 0.5m.
d) The smallest possible length of string is 1.0m
1) b,c 2) b,d 3) a,c 4) a,d
Pl explain the answer

Answer 1

*

Answer 2

Can't see the reply

Answer 3

well i just bookmarked the question. i will know when somebody answers it.

Answer 4

I hope the equation is
\[ y(x,t) = 4 \sin ( \pi x) \cos (\omega t) \]
Here is a demonstration of the wave
If you have Mathematica, you can try this code

` Animate[Plot[ 4 Cos[Pi x] Cos[3 t], {x, -5, 5}, `
` PlotRange -> {-5, 5}], {t, 1, 5}]`
The amplitude is the maximum value of displacement from the mean position. As you can see
\[ |4 \sin ( \pi x) \cos (\omega t)|\le 4 \cdot 1 \cdot 1 = 4 \]
The amplitude is 4.

For min length of the wire required, we need half wave length. For that .. keep t constant. Now we have
$$ 4 \cos ( \pi x ) $$
whose period is 2.
Hence the min-required string is 1mm