An unknown mass hangs on the end of a 2 m rope anchored to the ceiling when a strong wind causes the rope to vibrate and hum at its fundamental frequency of 100 Hz. If the rope has a mass of 0.15 kg, what is the unknown mass?

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.

In the following figure, what is the harmonic number of the standing wave? The wavelength of the standing wave? If the frequency of the standing wave is 30 Hz, what is the speed of the waves producing the standing wave?

By whipping a string up and down, you determine the fundamental frequency to be 4 Hz. If you attached the string to a motorized oscillator and increased the frequency to 28 Hz, how many loops would this standing wave have?

One of the harmonic frequencies for a particular string under tension is 325 Hz. The next higher harmonic frequency is 390 Hz. What harmonic frequency is next higher after the harmonic frequency 195 Hz?