Given: A snapshot at time t = 0 of a transverse sinusoidal traveling wave moving

Question

Given:

A snapshot at time t = 0 of a transverse sinusoidal traveling wave moving on a stretched string in the +x direction with speed v = 125 m/s is shown in the figure.  The tension in the string is F  =  400 N.  Assume that you can read the graph to three significant figures.

Find:

A) What are the amplitude A, wavelength , wave number k, angular frequency , frequency f, and period T of the wave?

B) What is the linear mass density µ of the string?

C) Write down the wave function for the transverse string wave versus both x and t.  

Please show work, lifesaver to the person who can help me. Thank you.

Explanation / Answer

(a) From the figure the amplitude of wave is equal to the

A = 3 cm

Wave length of wave = 8 ( 0.1 m)

= 0.8 m

wave number k= 2/ = 2/0.8 m

= 7.85 /m

The speed of wave v = f

then frequency f = v/ = 125 m/s / 0.8 m

= 156.25 /s

Angular frequency = 2f = 2(156.25)

= 981.75 rad/s

Time period T = 1/f = 1/156.25 = 0.0064 s

-------------------------------------------------------------------------------------

(b) The linear mass density

v = F/

= F/v2

= 400 N / (125 m/s)2

= 0.0256 kg/m

(c) The wave function

y = A cos ((7.85/m) x - (981.75 rad/s) t)

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.