PHYS 261 Lecture Notes - Lecture 8: Velocity Factor, Transverse Wave, Angular Frequency

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mauverat885

9 Apr 2019

School

University of Maryland

Department

Physics

Course

PHYS 261

Professor

Matthew Severson

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Document Summary

Transverse wave along string in x direction causes a displacement in the y direction that varies with time and position on the string. A = wave amplitude k = 2pi/ (wave number) = 2*pi*f (angular frequency) v = f (wave propagation speed) If a second wave is moving along the string at the same time, then the result is the sum of the two waves at each point. 2nd wave in opposite direction (-x direction), same a, same f. For 2 waves in opposite directions but same a. Superimposing 2 waves in opposite direction but same a. Antinodes: where kx is odd multiple of pi/2 and string has amp = 2a. Nodes: where kx is multiple of pi and y=0 (not moving) For a string clamped at 2 ends, must be a node at each end. If it starts at x=0 and ends at x=l then: Resonance frequencies on a string of length l:

Related Questions

1) The equation of a transverse wave on a string is
y = (2.0mm) sin[(20 m-1)x - (600 s^-1)t]

The tension in the string is 15 N. (a) What is the wave speed?(b) Find the linear density of this string in grams per meter.

2) What phase difference between two identical traveling waves,moving in the same direction along a streched string, results inthe vombined wave having an amplitude 1.50 times that of the commonamplitude of the two combining waves? Express your answer in (a)degress, (b) radians, and (c) wavelengths.

3) A rope, under a tension of 200 N and fixed at both ends,oscillates in a second-harmonic standing wave pattern. Thedisplacement of the rope is given by

y= (0.10 m (sin Ï/2) sin 12Ït,

where x=0 at one end of the rope, x is in meters, and t is inseconds. What are (a) the lenght of the rope, (b) the speed of therope, and (c) the mass of the rope ? (d) If the rope oscillates ina third-harmonic standing wave pattern, what will be the period ofoscillation?

A transverse sinusoidal wave is moving along a string in thepositive direction of an x axis with a speed of 80 m/s. At t = 0,the string particle at x = 0 has a transverse displacement of 4.0cm from its equilibrium position and is not moving. The maximumtransverse speed of the string particle at x = 0 is 16 m/s.
(a) What is the frequency of the wave?
(b) What is the wavelength of the wave?

If y(x,t) = y_m sin(kx Â± Ït + Ï) is the form of the waveequation,

What are

A string of length (L) and mass (M) vibrating with a linearfrequency (f) and amplitude (A) has a periodic transversedisturbance traveling its length at a speed (v).

L = 2.00 meters = length of string
M = 0.005 kg = mass of string
f = 100 Hz = linear frequency of vibration
A = 0.030 meters = amplitude of the period transverse wavetraveling in the string
v = 20 m/s = speed of the transverse wave traveling down thestring

Determine the following:
a) Wavelength of the periodic disturbance
b) Wave number
c) Tension in the string
d) Fundamental frequency in the string
e) Maximum transverse speed and maximum transverse acceleration ofany small bit of string
f) Displacement of the bit of string at x = L/4 when t = 0.5seconds
g) Speed of the bit of string at x = 3L/4 when t = (1/80)seconds
h) Average total energy of waves on the string
i) Average rate at which energy is transmitted along the string

PHYS 261 Lecture Notes - Lecture 8: Velocity Factor, Transverse Wave, Angular Frequency

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