Question

16.
abic
The vibration of a string fixed at both ends are described by Y = 2 sin (piex) sin(100piet) where Y is
in mm, xis in cm, t in sec, then
a) Maximum displacement of the particle x = 1/6 cm would be 1 mm
b) Velocity of the particle at x = 1/6 cm at time t = 1/600 sec will be 15773 mm/s.
c) If the length of the string be 10 cm, number of loop in it would be 5
d) None of these
a
nd​

Answer 1

Answer:

Maximum displacement of the particle x=1/6cm would be 1mm

Step-by-step explanation:

The general equation of a standing wave is:

y=2Asin(ωt)cos(kx+θ); The cosines and sines are easily interchangeable by just adding a phase.

It can be easily manipulated into:

y=2Asin(ωt)sin(−kx+θ);

Comparing with the given equation, we get k=−π and ω=100π;

From this we get λ=2π/k=2cm;

In 10cm of rope, there would be 10/2=5 wavelength and twice the number of loops. i.e. 10 loops.

Putting x=1/6 in the given equation, it reduces down to

y=2sin(

6

π

)sin(100πt);

y=1sin(100πt);

From this we can see that:

Maximum displacement is 1mm;

velocity = 100πcos(100πt);

hope it help you

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