a. Write down an equation, D(x, t), for a transverse standing wave on a string of length L = 0.20 m that is fixed at each end, given that the antinodes are at maximum displacement at t = 0. The standing wave has wavelength 2 = 0.20 m and frequency f= 400 Hz. The maximum displacement of an antinode is 0.040 m.

Principles of Physics: A Calculus-Based Text
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Chapter13: Mechanical Waves
Section: Chapter Questions
Problem 14P: A transverse sinusoidal wave on a string has a period T = 25.0 ms and travels in the negative x...
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a. Write down an equation, D(x, t), for a transverse standing wave on a string
of length L = 0.20 m that is fixed at each end, given that the antinodes are
at maximum displacement at t = 0. The standing wave has wavelength 2
= 0.20 m and frequency f= 400 Hz. The maximum displacement of an
antinode is 0.040 m.
%3D
b. What is the period T of this wave?
c. Draw a sketch of the standing wave at the following times t = 0, t= T/4, t
= T/2.
d. What are the values of x for all antinodes?
e. What are the values of x for all nodes?
f. Write down the equation for the two traveling waves that make up this
standing wave.
g. What is the speed of these travelling waves?
Transcribed Image Text:a. Write down an equation, D(x, t), for a transverse standing wave on a string of length L = 0.20 m that is fixed at each end, given that the antinodes are at maximum displacement at t = 0. The standing wave has wavelength 2 = 0.20 m and frequency f= 400 Hz. The maximum displacement of an antinode is 0.040 m. %3D b. What is the period T of this wave? c. Draw a sketch of the standing wave at the following times t = 0, t= T/4, t = T/2. d. What are the values of x for all antinodes? e. What are the values of x for all nodes? f. Write down the equation for the two traveling waves that make up this standing wave. g. What is the speed of these travelling waves?
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