The A-string on a guitar is 0.648 m long and has a linear mass density of 4.25 g/m. If the string is perfectly in tune, then the third harmonic should have a frequency of 330 Hz. However, on a particular out-of-tune guitar, the A-string's third harmonic is measured to be 319 Hz. By how much should the tension be increased in order to bring the A-string back into tune? (You may ignore any slight changes to the linear mass density of the string that might result from the tuning process.)

A string consists of two parts attached at x=0. The right part of the string has mass per unit length 12.8 g/m and the left part has mass per unit length 3.2g/m. The string tension is T. If a wave of amplitude 3.5cm travels along the left part of the string, what is the amplitude of the wave that is transmitted to the right part of the string?

Two identical guitar strings are prepared such that they have the same length (0.67 m) and are under the same amount of tension. The first string is plucked at one location, primarily exciting the fourth harmonic. The other string is plucked in a different location, primarily exciting the second harmonic. The resulting sounds give rise to a beat frequency of 369 Hz. What is the wave propagation speed on the guitar strings?

A 120-cm string has a total mass of 80 g.  One end of the string is tied to a post.  A pulley is placed 90 cm from the post, and a mass of 265 g is suspended from the other end of the string, and hung over the pulley.  (a) What do you expect the speed of waves on the string to be equal to?  (b)  What is the frequency of a standing wave on this string which has four antinodes?

A string of length 100.0 cm is fixed at both ends and is kept under a tension of 25.00N. The linear mass density of the string is 0.650 g/m.(a) What is the lowest resonant frequency of the string?(b) What are the frequencies of the second and third harmonics?(c) What is the wave speed for this string?(d) What is the lowest resonant frequency when the tension is increased to 35.00N?

A thick power line of length 75 m is stretched taut between two poles, experiencing a tension force of 6250 N. The mass of the power line 750 kg. What is the maximum resonate frequency of the cable if the wavelength is exactly 1/3 the length of the cable?

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 stretched string fixed at each end has a mass of 37.0 g and a length of 9.00 m. The tension in the string is 44.0 N. (a) Determine the positions of the nodes and antinodes for the third harmonic. (Enter your answers from smallest to largest distance from one end of the string.)nodes:  ?m ? m  ? m ? m antinodes: ? m  ?m  ?m (b) What is the vibration frequency for this harmonic? ?Hz

A A-string on a particular guitar has a circular cross-section with a diameter of 0.914 mm. The vibrating length of the string is 65.0 cm.   (1) If the density of the string is 7,600 kg/m3, find the mass per unit length of the string.   (2) For the string to be in tune, it should have a natural frequency of 110.00 Hz. Find the tension in the string that produces this natural frequency.  (3) Assuming that the guitar string is in tune, find the frequency and wavelength of the 5th harmonic.

Suppose the strings on a violin are stretched with the same tension and each has the same length between its two fixed ends. The musical notes and corresponding fundamental frequencies of two of these strings are G (196.0 Hz) and E (659.3 Hz). The linear density of the E string is 7.74 x 10-4 kg/m. What is the linear density of the G string?