The linear density of a string is 3.20 x 10^(-3) kg/m. A speaker is used to driv

Question

The linear density of a string is 3.20 x 10^(-3) kg/m. A speaker is used to drive the string so that each piece of string completes 13.0 oscillations per second. An enterprising young physics student measures the wavelength of the wave to be 45.0cm and the amplitude of the wave to be 1.50 cm and notes that the wave is traveling ot the left.

A) find how fast the wave travels down the string.
B) Find the tension in the string.

C) Write down equation of motion for the string undergoing the motion described. HINT: Use general y(x,T) for a wave on a string then substiture in appropriate values. Assume there is NO phase angle for the string.

D) Find the velocity of a piece of string located at x=10.0cm at at time 8 x 10^(-3) s.

Explanation / Answer

A )

frequency, f = 13 Hz

speed = wavelength * f

           = 0.45 m (13 Hz) = 5.85 m/s

B) v = sqrt[ T / linear density ]

5.85 = sqrt[ T / (3.20 x 10^-3 ) ]

T = 0.11 N

c) y(x,t) = sin(kx - wt)

w = 2 pi f = 26 pi

k = 2pi/ lambda = 2 pi / 0.45 =4.44 pi

y (x ,t) = 1.50 cm sin(4.44pi x - 26pi t )

D)

v = dy/dt = 1.50 x 26 x pi cos(4.44pi x - 26pi t )

v = 123 cm/s cos(4.44pi x - 26pi t )

at x = 0.10 m and t = 8 x 10^-3 sec

y(x,t) = 123cm/s cos[ (4.44 x pi x 0.10) - (26 x pi x 8 x 10^-3)]

     = 90.4 cm/s Or 0.904 m/s

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

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