Standing Sound Waves Practice Problems

A musical note having a fundamental frequency of 300 Hz is played by blowing air into an open-ended bamboo wind instrument. Find the new fundamental frequency (f₁, _new) if one end is closed with the hand.

An open-ended tube producing a second harmonic frequency of 380 Hz is suddenly closed at one end. Calculate the first harmonic wavelength (λ) of the stopped tube.

 A musical instrument consisting of a long metallic conduit has both ends open. The instrument produces a first harmonic frequency of 250 Hz. Find the length (L) of the conduit.

A plumber whistles into the right open end of a metal tube of length 3 m and generates standing waves. Draw a diagram showing the locations of the displacement nodes and antinodes along the tube for the fundamental and first overtone. The left end of the tube is closed.

A woodwind player generates standing waves in a 32-cm flute. The resonating air column is open at both ends. Draw a diagram showing the locations of the displacement nodes and antinodes along the flute for the first and second harmonic.

What is the shock wave angle produced in the water just after a high-speed drone traveling at 9500 m/s enters a lake? Assume the water temperature is 25°C. [Hint: the speed of sound in water is 1560 m/s].

A cello string produces a frequency of 650 Hz when vibrating at its second harmonic. If a cellist shortens the effective vibrating length of the string to 80% of its original length by pressing down on the fingerboard, what will be the new fundamental frequency of the string?

Determine whether a specific flute design is open or closed and what it's length will be if it is surrounded by air at a temperature of 22.5°C and produces successive harmonics at 408 Hz and 452 Hz?

What is the fundamental frequency of a uniform narrow 1.60 m long tuning pipe, that is open at both ends, and resonates at two successive harmonics of 285 Hz and 340 Hz?

A violin string is 0.32 m long and is tuned to play D above middle C (290 Hz). A fret is at a particular distance from the end of the string on which if the finger is placed G above middle C (390 Hz) can be played. Calculate the wavelength on the string of this 390-Hz wave.

An instrument called a Sitar has strings that are generally about half a meter long. One such string plays D (294 Hz) when untouched but can be made to play E (330 Hz) if fingered at a certain point. Calculate the frequency and wavelength of the string fingered at the same position if played in an environment with a temperature of 18.0°C.

A cello string is typically a length of 0.70 m. A particular cello string is tuned to play the note A which is 220 Hz when it is unfingered. At what distance from the end of the string must one position their finger on the string in order to play the note C4 which is 260 Hz?

An asteroid enters Earth's atmosphere at a velocity of approximately 18000 km/hr. What would be its mach angle given that on Earth, the speed sound travels at roughly 340 m/s?

A student is experimenting with a 2.00 m long pipe that has both of its ends open, and that contains some unknown gas inside. Investigating further, she discovers that the pipe has two consecutive harmonic frequencies of 150 Hz and 200 Hz. Calculate the speed of sound in the gas in the pipe.

A fighter jet flying at an altitude of 2.0 km above ground level breaks the sound barrier. By the time its sonic boom reaches the person standing on the ground exactly below the jet, the jet has already covered a horizontal distance of 3.0 km away. Determine (i) the angle made by the shock cone, (ii) the speed at which the jet was traveling along with its Mach number. Assume that the speed at which sound travels in air is approximately equal to 340 m/s.

A musician, riding a bicycle moving away from you at 26 m/s, plays a flute that produces sound by setting up the fundamental standing wave in an air column 7.40 cm long. What frequency do you hear if the flute is closed at one end? Assume that the speed of sound in air is 343 m/s.

A guitarist has a string with a fundamental frequency of 450 Hz and a vibrating portion length of 34 cm. To play a note at 599 Hz, how far from the end of the string should the guitarist place their finger?

A cello string measuring 75 cm in length is tuned to a fundamental frequency of 220 Hz. When a cellist presses the string 25 cm from the bridge, the pitch produced is 660 Hz. If the cellist uses the "vibrato" technique, moving his finger 0.60 cm to either side, what frequencies will be generated?

An acoustics engineer is testing the impact of different gases on the resonance properties of a two-sided open pipe used in a musical instrument. Initially, the pipe is filled with neon at 0°C, and the engineer records a fundamental frequency of 980 Hz. To further analyze the effects of different gases on the instrument's sound, the engineer decides to fill the pipe with nitrogen at the same temperature of 0°C. Determine the frequency of the two-sided open pipe when it is filled with nitrogen at 0°C.

Speed of sound at 0°C in various gases

• Nitrogen (N₂): 353 m/s
• Neon (Ne): 433 m/s

Two students are examining the properties of sound using a cylindrical resonance chamber that is modeled as a 200 cm long open closed tube. The experiment begins with the chamber's air temperature at 27°C. As the students introduce heat to the chamber, the air temperature inside the tube rises, causing the speed of sound to reach 361 m/s. Determine if the fundamental frequency of the resonance chamber increases or decreases, and by what amount. Take the speed of sound in air at 27°C to be 330 m/s.

A physics teacher conducts a lab experiment with a 200 cm long pipe, one end open and the other closed, to demonstrate standing sound waves to her students. The teacher creates a standing sound wave with a frequency of 213 Hz inside the pipe under conditions where the speed of sound is 340 m/s. She tasked the students with determining the following:

i) The number of pressure antinodes inside the pipe.

ii) The distance of each antinode from the open end of the pipe.

Recent studies have shown that sounds similar to natural speech can be synthesized using a closed-pipe system. The closed pipe system will mimic the human vocal tract. A research team investigating the effect of gas variation on the frequencies of produced sounds used a closed pipe filled with different gases at room temperature. In the first experiment, the closed pipe is filled with argon. A vibrating blade produces two standing waves with frequencies of 345 Hz and 1685 Hz. The experiment is repeated with hydrogen gas inside the closed pipe. Determine the frequencies produced when the closed pipe is filled with hydrogen. At room temperature, the speed of sound for argon is 319 m/s and for hydrogen, it is 1270 m/s.

A collimated sound beam of frequency 340 Hz enters the open end of a U-shaped pipe, as shown in the figure. The experiment is done at room temperature. The two parallel parts of the U-shaped tube are separated by a distance of 15 cm and connected by a round turn. The parallel tubes have an initial length of 65 cm. The length could be extended by the same amount, l, on each side. The maximum extension is 65 cm. On the other open end, a sound level meter is used to detect the transmitted waves. Calculate the possible values of l for which the sound level meter picks up the highest level of sound.

A 450 Hz pure sound wave is directed toward the upper end of a graduated glass cylinder held straight up. The glass cylinder of 130 cm in height is totally filled with oil and has a tap at the base. The oil is at room temperature. The oil is drained gently from the tap. We are expecting that standing waves will be generated inside the cylinder at specific oil levels, h. The level h is measured from the base. Calculate the values of h.

A pipeline technician responsible for the maintenance of oil and gas pipeline systems developed a method to measure the length of underground empty pipes based on standing waves. In one experimental test, the technician sent adjustable frequency sound from the open end of a pipeline and detected standing wave signals at 6.07 Hz and 7.80 Hz using standing wave detection apparatus, with no other resonance frequency in between. Calculate the length of the pipeline. Assume the pipeline is an open-closed tube with a sound speed of 340 m/s inside the empty pipe.

To tune notes of varying pitches, most wind instruments have a mechanism for adjusting the length of the air column. A musician adjusts the length of his open-open instrument to produce a fundamental frequency of exactly 494 Hz on a day when the speed of sound in the air was 343 m/s. The concert was held on a different day. The speed of sound in the air decreased to 338 m/s. How much the musician must adjust the length of his musical instrument to obtain the same frequency obtained during the day?