Question

1) A standing-wave pattern is observed in a thin wire with a length of 4.00 m. The wave function is y = 0.002 00 sin (πx) cos (100πt) where x and y are in meters and t is in seconds.

(a) How many loops does this pattern exhibit?

(b) What is the fundamental frequency of vibration of the wire?

Answer 1

__________________________

(a)

y = 0.002 00 sin (πx) cos (100πt)

general equation

y = 2r Sin(2πx/) Cos(2πvt/)

comparing the two equations

2π/ = π

= 2

L = 4 m

n = number of loops = 2L/ = 2 x 4/2 = 4 loops

__________________________

(b)

comparing the equations

2πv/ = 100π

2v/2 = 100

v = 100

for n = 1

= 8

fundamental frequency is given as

f = v/ = 100/8 = 12.5 Hz

__________________________

Please rate

if any mistake in this answer please comment i will clarify your doubt . thank you