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05:42A guitar string is 91 cm long and has a mass of 3.2 g. The vibrating portion of the string from the bridge to the support post is ℓ = 64cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?
A particular string resonates in four loops at a frequency of 320 Hz. Name at least three other frequencies at which it will resonate. What is each called?
One end of a horizontal string is attached to a small-amplitude mechanical 60.0-Hz oscillator. The string’s mass per unit length is 3.9 x 10⁻ ⁴ kg/m. The string passes over a pulley, a distance ℓ = 1.50 m away, and weights are hung from this end, Fig. 15–38. What mass m must be hung from this end of the string to produce five loops of a standing wave? Assume the string at the oscillator is a node, which is nearly true.
Suppose two linear waves of equal amplitude and frequency have a phase difference ϕ as they travel in the same medium. They can be represented by: D₁ = A sin (kx - ωt); D₂ = A sin ( kx - ωt + ϕ). Describe the resultant wave, by equation and in words, if ϕ = π/2.
Suppose two linear waves of equal amplitude and frequency have a phase difference ϕ as they travel in the same medium. They can be represented by: D₁ = A sin (kx - ωt); D₂ = A sin ( kx - ωt + ϕ). What is the amplitude of this resultant wave? Is the wave purely sinusoidal, or not?
The displacement of a standing wave on a string is given by D = 2.4 sin ( 0.60x ) cos (42t) , where x and D are in centimeters and t is in seconds. What is the distance (cm) between nodes?
