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Boundary conditions of standing waves

         

If two adjacent resonant frequencies are \(440\) and \(330\text{ Hz}\) for a string which is stretched to a length of \(77.0\text{ cm},\) what is the lowest resonant frequency?

Consider a wire with length \(8.0\text{ m}\) and mass \(110\text{ g}\) which is under a tension of \(290\text{ N}.\) What are the lowest and the third lowest frequency for a standing wave on the wire?

Consider two identical sinusoidal waves with the same wavelength and amplitude traveling in opposite directions along a string with a speed of \(30.0 \text{ cm/s}.\) If the time interval between adjacent instants when the string is flat is \(0.100\text{ s},\) what is the wavelength of the waves?

If a string with length \(5.50\text{ m},\) mass \(0.120\text{ kg},\) and tension \(98.0\text{ N}\) is oscillating, approximately what are the longest possible wavelength and frequency for a standing wave?

Suppose that a string, two ends of which is fixed at a distance of \(D=120.0\text{ cm},\) has a linear density of \(7.4\text{ g/m}\) and is under a tension of \(150\text{ N}.\) If the string is oscillating in a standing wave pattern, as shown in the above figure, what is the approximate frequency of the traveling waves?

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