Physics 112 HW23
Due Friday, 24 April 2015
U1-SW1: (Wolfson 1st ed., Ch. 14 Ex. 38 plus my pt c) A 2.0m long string is clamped
at both ends.
a) What is the longest-wavelength standing wave that can exist on this string?
b) If the wave speed is 56 m/s, what is the lowest standing wave frequency?
c) What are the wavelength and frequency of the standing wave with 6 antinodes?
U1-SW1A: A 2.0 m long string is clamped at one end, but free at the other. The free
end is attached to a ring of negligible mass that slides frictionlessly along a vertical rod
(much like in the diagram below).
a) What is the longest-wavelength standing wave that can exist on this string?
b) If the wave speed is 56 m/s, what is the lowest standing wave frequency?
c) What are the wavelength and frequency of the standing wave with 6 antinodes?
U1-SW1B: A 2.0 m long string is free at both ends. The free ends are attached to rings
of negligible mass that slide frictionlessly along vertical rods.
a) What is the longest-wavelength standing wave that can exist on this string?
b) If the wave speed is 56 m/s, what is the lowest standing wave frequency?
c) What are the wavelength and frequency of the standing wave with 6 antinodes?
U1-SW4: A string 1 m long is clamped at one
end. The other end is attached to a ring of
negligible mass which encircles a rod.
There is no friction between the rod and the
ring. The string has µ = 10 g/m and the
force of tension in the string is 1000N.
Your finger touches the string at a point 2/3
the length of the string from the clamped
end, essentially forcing a node there. Determine the lowest two resonant frequencies
of the string.
U1-SWMP: Consider a circular string with μ = 0.007 kg/m and radius r = 1m. In other
words, this is a string that has no ends, and is arranged in a circle. Assume it remains
circular, but has a constant tension T = 100N throughout its length.
a) What is the smallest-frequency standing wave that can exist on this string? (No
kinks in the string are allowed!)
b) Derive (figure out) a formula for the allowed standing wave frequencies in this
string. Your formula may only contain n (the number of antinodes), r, T, and μ.
c) What are the wavelength and frequency of the standing wave with 6 antinodes?
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