Question

A wave on a string is described by

*y*(*x*,*t*)=( 4.0 cm
)×cos[2*π*(*x*/( 1.2 m )+*t*/( 0.30 s ))] ,
where *x* is in m and *t* is in s .

**Part B**

What is the wave speed? v = m/s

**Part C**

What is the wave frequency? f = Hz

**Part D**

What is the wave length? = m

**Part E**

At *t* = 0.75 s , what is the displacement of the string
at *x* = 0.10 m ? d
= cm

Answer #1

We know that standard wave equation is given by:

y(x, t) = A*cos ((2*pi/)*x + (2*pi/T)*t)

y(x, t) = A*cos (k*x + w*t)

Given wave equation is:

y(x, t) = (4.0 cm)*cos (2*pi*(x/1.2 + t/0.30))

Part B.

wave speed is given by:

V = /T

from given equation: = wave length = 1.2 m

T = time period = 0.30 sec

So,

V = 1.2/0.30

**V = 4.0 m/s = wave speed**

Part C.

Wave frequency will be:

f = 1/T

**f = 1/0.30 = 3.33 Hz**

Part D.

wave length will be:

**
= wavelength = 1.2 m**

Part E.

At x = 0.10 m and t = 0.75 sec, displacement of string will be:

y(0.10, 0.75) = (4.0 cm)*cos (2*pi*(0.10/1.2 + 0.75/0.30))

**y(0.10, 0.75) = -3.464 cm = -3.5 cm**

**Let me know if you've any query.**

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