A uniform cylindrical steel wire, 55.0 cm long and 1.14 mm in diameter, is fixed at both ends. To what tension must it be adjusted so that, when vibrating in its first overtone, it produces the note D-sharp of frequency 311 Hz? Assume that it stretches an insignificant amount.

A string clamped at two ends is vibrating at a fundamental frequency of 443.5 Hz such that the distance between adjacent nodes is 44 cm. The tension of the wire is 93 N and wire diameter is 0.4 mm. Calculate the density of the material of the wire and give your answer in SI units.

A string vibrates at its fifth-harmonic frequency as it makes a standing wave. The amplitude at a point 40 cm from one end is three-quarters of the maximum amplitude. How long is the string?

Two identical piano wires have a fundamental frequency of 555 Hz when kept under the same tension. What fractional increase in the tension of one wire will lead to the occurrence of 7 beats/s when both wires oscillate simultaneously?

A 2.00-m-long wire having a mass of 0.100 kg is fixed at both ends. The tension in the wire is maintained at 20.0 N. (a) What are the frequencies of the first three allowed modes of vibration (standing waves)? (b) If a node is observed at a point 0.400 from one end, in what mode and with what frequency is it vibrating? (c) If this wire can be used to create a sound wave as part of a musical instrument, what is the frequency and wavelength of the sound wave created if the string is oscillating in its fundamental mode?

The G string on a guitar is a 0.46 mm diameter steel string with a linear density of 1.3 g/m. When the string is properly tuned to 196 Hz, the wave speed of the string is 250 m/s. Tuning is done by slowly tightening the string, and stretching it in the process. By how many mm does a 75 cm-long G string stretch when it is first tuned? [Hint: Look up relevant properties of steel as needed.]

A string of mass 16.6 grams and length 0.74 meters and fixed at the ends is under tension 243 N. What is the vibrational frequency of n= 4 harmonic?

A heavy stone is hung from the ceiling by a wire mass of 8.35g and length 70.7 cm. When you pluck the upper end of the wire, a pulse travels down the wire, taking 3.89ms to reach the lower end. Find the mass in kilograms of the stone. Use at least three significant figures.

A string that is stretched between fixed supports separated by 51.4 cm has resonant frequencies of 792.0 and 594.0 Hz, with no intermediate resonant frequencies. What are (a) the lowest resonant frequency and (b) the wave speed?

The g string in a violine is 30cm long. The tension on the G string is 90N. when playing without fingering. It vibrates at a frequency f 196 hertz (assuming that it vibrates in its fundamental). The next higher notes on the C-major scale are A (220Hz) and b (247Hz) What is the mass per meter (mass density) of the G-string How far from the end of the string must a finger be placed to play the A note.