18. Waves & Sound

Two strings on a musical instrument are tuned to play at 392 Hz (G) and 494 Hz (B).

(a) What are the frequencies of the first two overtones for each string?

Two strings on a musical instrument are tuned to play at 392 Hz (G) and 494 Hz (B).

(c) If the strings, instead, have the same mass per unit length and are under the same tension, what is the ratio of their lengths (ℓ_G / ℓ_B)?

(II) 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 (c) five loops of a standing wave? Assume the string at the oscillator is a node, which is nearly true.

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A transverse wave pulse travels to the right along a string with a speed v = 2.4 m/s . At t = 0 the shape of the pulse is given by the function

D = 4.0m³ / (x² + 2.0m²) ,

where D and x are in meters.

(b) Determine a formula for the wave pulse at any time t assuming there are no frictional losses.