From the mathematical functions (with x is in metres, t in seconds), select thos

Question

From the mathematical functions (with x is in metres, t in seconds), select those which correspond to each of the five motions below . For example, if functions A and G satisfy motion 1, function C satisfies motion 2 and none of the functions satisfies motions 3, 4 and 5, enter AGCNNN. (Note that the answers for each motion must be in alphabetical order.)

A) y(x,t) = 0.4 sin(2x)cos(6t)0.8 sin(x)cos(x)cos(6t)

B) y(x,t) = 0.4 cos(2x)sin(6t)

C) y(x,t) = 0.4

D) y(x,t) = 0.2 sin(3x9t)

E) y(x,t) = 0.4 cos(x)sin(t/3)

F) y(x,t) = 0.4 sin(2x)cos(2t/6)

G) y(x,t) = 0.8/(2+(3x+9t)2)

H) y(x,t) = 0.4/(1+(x3t)2)

N) none of the above

1) A motion in which the movement of the medium corresponds to a wavelength of 1 m.

2) A harmonic travelling wave or wave pulse which causes the medium to oscillate with a standard frequency of 3 Hz.

3) A standing wave that causes the medium to oscillate with a standard frequency of 3 Hz.

4) A harmonic wave or wave pulse travelling in the positive x direction at 3 m/s.

5) A motion in which the medium at x = 0 m is fixed, i.e., it is unable to move.

From the mathematical functions, select those which correspond to each of the five motions below For example, if fractions A and G satisfy motion function C satisfies motion and none of the function satisfy motions 3 4 and 5, enter AGCNNN. A motion in which the movement of the medium corresponds to a wavelength of 1 m. A harmonic travelling wave or wave pulse which causes the medium to oscillate with a standard frequency of 3 Hz A standing wave that causes the medium to oscillate with a standard frequency of 3 Hz A harmonic wave or wave pulse travelling in the positive x direction at 3 m/s. A motion in which the medium at x = 0 m is fixed, i.e.. it is unable to move.

Explanation / Answer

equation of a standing wave; y= a sin kx cos wt

k= 2 pi/lambda and w= 2 pi/T oe w= 2 pi f

1) A motion in which the movement of the medium corresponds to a wavelength of 1 m

B) y(x,t) = 0.4 cos(2x)sin(6t)

here 2= 2 pi/lambda, so lambda= 1m

F) y(x,t) = 0.4 sin(2x)cos(2t/6)

here 2= 2 pi/lambda, so lambda= 1m

so both function B and F satisfy 1

(2) A harmonic travelling wave or wave pulse which causes the medium to oscillate with a standard frequency of 3 Hz.

none of the gven functions represents a travelling wave with a freq of 3 Hz , so N.

(3)A standing wave that causes the medium to oscillate with a standard frequency of 3 Hz

B) y(x,t) = 0.4 cos(2x)sin(6t)

2f=6   

f= 3 Hz, so for 3, we have B .

4) A harmonic wave or wave pulse travelling in the positive x direction at 3 m/s.

D) y(x,t) = 0.2 sin(3x9t)

2 pi /lambda= 3

lambda= 2pi/3

2pi f= 9

f= 9/2pi

wave velocity= f* lambda

v=(9/2pi)* (2 pi/3)

v= 3m/s

so for 4, it is D .

(5) A motion in which the medium at x = 0 m is fixed, i.e., it is unable to move.

C) y(x,t) = 0.4

we have C .

so the answer is BFNBDC

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