18. Waves & Sound

A 65-cm guitar string is fixed at both ends. In the frequency range between 1.0 and 2.0 kHz, the string is found to resonate only at frequencies 1.2, 1.5, and 1.8 kHz. What is the speed of traveling waves on this string?

A guitar string is 91 cm long and has a mass of 3.2 g. The vibrating portion of the string from the bridge to the support post is ℓ = 64cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?

The displacement of a standing wave on a string is given by D = 2.4sin(0.60x)cos(42t), where x and D are in centimeters and t is in seconds. Give the amplitude, frequency, and speed of each of the component waves.

The figure below shows a standing wave on a 2.0-m-long string that has been fixed at both ends and tightened until the wave speed is 40 m/s. What is the frequency of this wave?

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?

When you slosh the water back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 45-cm-wide tub is 0.85 Hz. What is the speed of the water wave?

The fundamental frequency of a violin string is 441 Hz when unfingered. What is its fundamental frequency if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a 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?

A wire with mass 40.0 g is stretched so that its ends are tied down at points 80.0 cm apart. The wire vibrates in its fundamental mode with frequency 60.0 Hz and with an amplitude at the antinodes of 0.300 cm. What is the speed of propagation of transverse waves in the wire?

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?

A 3m-long rope is stretched between two supports with a tension that makes the speed of transverse waves 60 m/s. What are the wavelength and frequency of the second overtone?

What are the three longest wavelengths for standing waves on a 60 cm long string that is fixed at both ends?

The two highest-pitch strings on a violin are tuned to 440 Hz (the A string) and 659 Hz (the E string). What is the ratio of the mass of the A string to that of the E string? Violin strings are all the same length and under essentially the same tension.

Piano tuners tune pianos by listening to the beats between the harmonics of two different strings. When properly tuned, the note A should have a frequency of 440 Hz and the note E should be at 659 Hz. What is the frequency difference between the third harmonic of the A and the second harmonic of the E?

The displacement of a transverse wave traveling on a string is represented by D₁ = 4.2 sin (0.84 x - 47t + 2.1), where D₁ and x are in cm and t in s. Find an equation that represents a wave which, when traveling in the opposite direction, will produce a standing wave when added to this one.