What is the speed (in m/s) of sound in air at 7 degrees Celcius? (Use the simplified formula from the Overview page.)
What is the speed (in m/s) of sound in air at 28 degrees Celcius? (Use the simplified formula from the Overview page.)
What is the speed (in m/s) of sound in air at 50 degrees Celcius?(Use the simplified formula from the Overview page.)
A group of hikers hear an echo 0.81 seconds after they shout. If the air temperature is 7 degrees Celcius (like in question #1 above), how far away (in meters) is the mountain that reflected the sound wave?
A dolphin swimming in seawater at a temperature of 25 degrees Celcius emits a sound directed toward the bottom of the ocean 127 m below. What period of time (in seconds) passes before the dolphin hears an echo? The speed of sound in seawater is 1350 m/s Calculate your answer accurate to three decimal places.
The sound level 2.88 m from a point source is 80 dB. At what distance (in meters) will the sound level be 60 dB?
The dB level at a distance of 2.5 m from a sound source is 70 dB. What is the dB level at the distance of 5 m?
The dB level at a distance of 2.5 m from a sound source is 70 dB.What is the dB level at the distance of 7.5 m?
The dB level at a distance of 2.5 m from a sound source is 70 dB.What is the dB level at the distance of 10 m?
A stereo speaker that we shall consider as a small source emits sound waves with a power output of 108 W. Find the intensity (in W/m2) at a distance of 10.3 m from the source. Express your answer in scientific notation. Both blanks must contain a number. Calculate your answer to at least 4 significant digits.
Referring to the previous problem. Find the intensity level in decibels at this distance.
Extra Problem Set B
Problem 1:
A circus performer stretches a tightrope between two towers. He strikes one end of the rope and sends a wave along it toward the other tower. He notes that it takes the wave 0.685 s to reach the opposite tower 20.0 m away. If one meter of the wire has a mass of 0.370 kg, find the tension (in Newtons) in the tightrope.
Problem 2:
The Dingwaives family does not have much use for their old corded phone so they give it to their son Stan in order to conduct physics experiments. The phone cord is 2.06 m long and has a mass of 0.177 kg. Stan notices that a transverse wave pulse travels from the receiver to the phone box in 0.112 s. What is the tension (in Newtons) in the cord?
Problem 3:
Transverse waves with a speed of 47.3 m/s are to be produced on a stretched string. A 4.94-m length of string with a total mass of 0.058 kg is used. What is the required tension (in Newtons) in the string?
Problem 4:
(Referring to the previous problem.) Calculate the wave speed (in m/s) in the string (assuming the same mass and length) if the tension is 7.64 N.
Problem 5:
One end of a 3.01-meter long string is attached to a wall while the other end hangs over a pulley and is attached to a hanging 2.0-kg mass (which creates a tension of 19.6 N). The speed of the pulse on the string is observed to be 14.8 m/s. What is the mass (in grams) of the string?
Problem 6:
A physics teacher stretches a string to a length of 1.04 meters and uses a mechanical oscillator to vibrate the string in its 6th harmonic. If the oscillator's frequency is 613 Hertz, then what is the speed (in meters/second) at which the waves travel through the string?
Problem 7:
(Referring to the previous problem.) The same string held at the same tension is vibrated at a frequency of 306.5 Hertz to create a different standing wave pattern. Determine the wavelength (in centimeters) of waves for this particular frequency.
Problem 8:
A steel wire in a piano has a length of 0.683 m and a mass of 4.24 X 10-3 kg. To what tension (in Newtons) must this wire be stretched in order that the fundamental vibration correspond to middle C (frequency of middle C = 261.6 Hz on the chromatic musical scale)?
Problem 9:
A stretched string is 153 cm long and has a linear density of 0.0140 g/cm. What tension (in Newtons) in the string will result in a second harmonic of 455 Hz?
Problem 10:
A wire of mass .276 g is stretched between two points 69.7 cm apart. If the tension in the wire is 563 N, find the frequency (in Hertz) of the 5th harmonic.
Problem 11:
(Referring to the previous problem.) Determine the frequency (in Hertz) of the fundamental for this wire.
Problem 12:
A stretched string fixed at each end has a mass of 38.7 g and a length of 7.24 m. The tension in the string is 55.7 N. What is the vibration frequency (in Hertz) for this third harmonic?
Problem 13:
Two pieces of steel wire having identical cross sections have lengths of L and 2L. The wires are each fixed at both ends and stretched such that the tension in the longer wire is four times greater than that in the shorter wire. If the fundamental frequency in the shorter wire is 63 Hz, what is the frequency (in Hertz) of the second harmonic in the longer wire? (HINT: first determine how many times greater the speed of the tighter wire is than the less tight wire.)
Problem 14:
A stretched string of length L is observed to vibrate in 6 equal segments (i.e., with 6 antinodes between its ends) when driven by a 605-Hz oscillator. What oscillator frequency (in Hertz) will set up a standing wave pattern such that the string vibrates in 3 segments (3 antinodes)?
Problem 15:
A standing wave pattern is established in a string that is 234 cm long and fixed at both ends. The string vibrates in 4 segments (i.e., with 4 antinodes between its ends) when driven at 147 Hz. Determine the wavelength (in centimeters).
Problem 16:
(Referring to the previous problem.) What is the fundamental frequency (in Hertz) of this string?
Problem 17:
A string 51.2 cm long has a mass per unit length equal to 14 X 10-4 kg/m. To what tension (in Newtons) should this string be stretched if its fundamental frequency is to be 35.0 Hz? Calculate your answer to the fourth decimal place.
Problem 18:
(Referring to the previous problem.) To what tension (in Newtons) should this string be stretched if its fundamental frequency is to be 309.0 Hz?
Problem 19:
The fundamental frequency of a 161-cm section of string is 145 Hertz. Determine the frequency (in Hertz) of the 6th harmonic of a 80.5-cm section of the same string. (Hint: first calculate the speed of waves in this string.)
Problem 20:
When held at a tension of T, a 111-cm long string has a fundamental frequency of 239 Hertz. Suppose that the tension is increased by a factor of 2.9 without any alteration in the string length or mass per unit length. What would be the new fundamental frequency (in Hertz)?
Extra Problem Set C
Problem 1:
The fundamental frequency of an open organ pipe corresponds to 379.7 Hz. The third resonance of a closed organ pipe has the same frequency. What is the length (in centimeters) of the closed-end pipe? (Assume a speed of sound in air of 343 m/s.) (The 'third resonance' means the 'third harmonic.')
Problem 2:
An organ pipe open at both ends is vibrating in its third harmonic with a frequency at 817 Hz. The length of the pipe is 0.646 m. Determine the speed of sound (in m/s) in air in the pipe.
Problem 3:
Middle C has a frequency of 261.6 Hz. What is the length (in centimeters) of the shortest pipe open at both ends which would produce a sound of this frequency? (Assume a speed of sound in air of 343 m/s.)
Problem 4:
(Referring to the previous problem.) What would be the required length (in centimeters) if the pipe is closed at one end?
Problem 5:
A closed organ pipe is 3.37 m long. There are several frequencies between 20 Hz and 20,000 Hz at which this pipe will resonate? Determine the 5th highest frequency (in Hertz) within this range. (Assume a speed of sound in air of 343 m/s.)
Problem 6:
A pipe open at both ends has a fundamental frequency of 347 Hz when the temperature is 0 degrees Celsius. What is the length (in cm) of the pipe?
Problem 7:
(Referring to the previous problem.) What is the fundamental frequency (in Hertz) at a temperature of 22.7 degrees Celsius? (Use the simplified formula from the Overview page to determine the speed of sound in air.)
Problem 8:
A tuning fork is sounded above a resonating tube. The first resonant point is 13 cm from the top of the tube and the second is at 39 cm. What distance (in cm) from the top of the tube would the third resonant point be located? Assume a speed of sound in air of 343 m/s.)
Problem 9:
(Referring to the previous problem.) What is the frequency (in Hertz) of the tuning fork?
Problem 10:
An open-end resonator has a length of 30 centimeters. What fundamental frequency (in Hertz) would this resonator play? Sound waves travel at 343 m/s through the resonator.
Problem 11:
(Referring to the previous problem.) A second air column is 1.34 times longer. What is the frequency of its second harmonic (in Hertz)?
Problem 12:
A certain pipe organ is closed at one end and produces a fundamental frequency of 291 Hertz. What fundamental frequency (in Hertz) would the same length pipe produce if it were open at both ends?
Problem 13:
What is the lowest frequency (in Hertz) of the standing wave of sound that can be set up between two walls that are 8.51 meters apart if the temperature is 25 degrees Celsius? (Assume that the walls force a node upon the standing wave pattern at each end.)
Problem 14:
Determine the length (in cm) of a closed-end organ pipe that produces a 7th harmonic of 1090 Hertz. (Assume a speed of sound in air of 343 m/s.)
Problem 15:
(Referring to the previous problem.) What is the fundamental frequency (in Hertz) of an open-end organ pipe which is 1.43 times longer?
Problem 16:
A physics student is doing a resonance tube lab. She notices that resonance is observed for the first harmonic when the length of the closed-end air column is 21.9 cm. Determine the third harmonic frequency (in Hertz) for this air column. (Assume a speed of sound in air of 343 m/s.)
Problem 17:
A resonance tube is closed at one end and resonates with a third harmonic frequency of 688 Hertz. Determine the fundamental frequency (in Hertz) of a second tube which is open at both ends and the same length.
Problem 18:
(Referring to the previous problem.) What is the frequency (in Hertz) of the 6th harmonic of this second tube?
Problem 19:
The G string on a violin has a fundamental frequency of 196 Hz. It is 30.5 cm long and has a mass of 0.509 g. A nearby violinist fingers her identical violin until a beat of 3 Hz is heard between the two. What is the length (in centimeters) of her violin string? (HINT: fingering a string makes its 'vibrational length' shorter.)
Problem 20:
A guitar string with a vibrational speed of 515 m/s plays a fundamental frequency of 368 Hertz. Determine the third harmonic frequency (in Hertz) of a closed-end air column which is 2.01 times longer. (Assume a speed of sound in air of 343 m/s.)