Question

A wave on a string is described by
y(x,t)=( 4.0 cm )×cos[2π(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.