3. One end of a horizontal string is attached to a small-amplitude mechanical 75.0 Hz oscillator. The string's mass per unit length is 5.3 x 10-4 kg/m. the string passes over a pulley, a distance L = 1.75 m away, and weights are hung from this end. Assume the string at the oscillator is a node, which is nearly true, and that the string at the pulley is also a node. Oscillator L m a. Sketch the shape of the string for the fundamental (lowest possible frequency) standing-wave mode of vibration of this string. In this case, how many wavelengths fit on the string? b. What mass m must be hung from the right end of the string so that the string tension is what is needed to produce the standing wave that you drew in part (a) at the given 75 Hz oscillation frequency? c. Sketch the shape of the string for the second harmonic (next possible frequency above the fundamental) mode of vibration of this string. In this case, how many wavelengths fit on the string? d. What mass m must be hung from the right end of the string to produce the standing wave that you drew in part (c)?
3. One end of a horizontal string is attached to a small-amplitude mechanical 75.0 Hz oscillator. The string's mass per unit length is 5.3 x 10-4 kg/m. the string passes over a pulley, a distance L = 1.75 m away, and weights are hung from this end. Assume the string at the oscillator is a node, which is nearly true, and that the string at the pulley is also a node. Oscillator L m a. Sketch the shape of the string for the fundamental (lowest possible frequency) standing-wave mode of vibration of this string. In this case, how many wavelengths fit on the string? b. What mass m must be hung from the right end of the string so that the string tension is what is needed to produce the standing wave that you drew in part (a) at the given 75 Hz oscillation frequency? c. Sketch the shape of the string for the second harmonic (next possible frequency above the fundamental) mode of vibration of this string. In this case, how many wavelengths fit on the string? d. What mass m must be hung from the right end of the string to produce the standing wave that you drew in part (c)?
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Transcribed Image Text:3. þne end of a horizontal string is attached to a small-amplitude mechanical 75.0 Hz oscillator. The
string's mass per unit length is 5.3 x 10-4 kg/m. the string passes over a pulley, a distance L= 1.75 m
away, and weights are hung from this end. Assume the string at the oscillator is a node, which is nearly
true, and that the string at the pulley is also a node.
L
Oscillator
m
a. Sketch the shape of the string for the fundamental (lowest possible frequency) standing- wave mode
of vibration of this string. In this case, how many wavelengths fit on the string?
b. What mass m must be hung from the right end of the string so that the string tension is what is
needed to produce the standing wave that you drew in part (a) at the given 75 Hz oscillation frequency?
c. Sketch the shape of the string for the second harmonic (next possible frequency above the
fundamental) mode of vibration of this string. In this case, how many wavelengths fit on the string?
d. What mass m must be hung from the right end of the string to produce the standing wave that you
drew in part (c)?
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