Problem 20.52 A wave on a string is described by D ( x , t )=(2.2cm) sin[2 ? ( x

Question

Problem 20.52

A wave on a string is described by
D(x,t)=(2.2cm)
sin[2?(x/(6.0m)+t/(0.26s)+1)], where x is in m and t is in s.

Part A

In what direction is this wave traveling?

Part B

What is the wave speed?

Express your answer to two significant figures and include the appropriate units.

Part C

What is the frequency?

Express your answer to two significant figures and include the appropriate units.

Hz

Part D

What is the wave number?

Express your answer to two significant figures and include the appropriate units.

Part E

At t=0.78s, what is the displacement of the string at x=6.5m?

Express your answer to two significant figures and include the appropriate units.

Part A

In what direction is this wave traveling?

in the positive x-direction in the negative x-direction in other direction

Part B

What is the wave speed?

Express your answer to two significant figures and include the appropriate units.

v =

Part C

What is the frequency?

Express your answer to two significant figures and include the appropriate units.

f =

Hz

Part D

What is the wave number?

Express your answer to two significant figures and include the appropriate units.

k =

Part E

At t=0.78s, what is the displacement of the string at x=6.5m?

Express your answer to two significant figures and include the appropriate units.

D(6.5m,0.78s) =

Explanation / Answer

comaparin g it to standard equation

Y = A sin( kx+wt +c)

A ) in the negative x-direction

B ) wave speed = 6/0.26 = 23.076m/sec

C) from equation

w = 1/0.26 = 3.846 rad/sec

T = 2pi/w = 1.6336 sec

D ) from the equation

K = 1/6 = 0.167

E ) displacement at D(6.5m,0.78s) = -2.05036 cm

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