Boundary conditions of standing waves

         

If two adjacent resonant frequencies are 440440 and 330 Hz330\text{ Hz} for a string which is stretched to a length of 77.0 cm,77.0\text{ cm}, what is the lowest resonant frequency?

Consider a wire with length 8.0 m8.0\text{ m} and mass 110 g110\text{ g} which is under a tension of 290 N.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 cm/s.30.0 \text{ cm/s}. If the time interval between adjacent instants when the string is flat is 0.100 s,0.100\text{ s}, what is the wavelength of the waves?

If a string with length 5.50 m,5.50\text{ m}, mass 0.120 kg,0.120\text{ kg}, and tension 98.0 N98.0\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 cm,D=120.0\text{ cm}, has a linear density of 7.4 g/m7.4\text{ g/m} and is under a tension of 150 N.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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