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Worksheet: Normal Vibrational Modes

Q1:

An organ pipe of length 3.00 m is closed at both ends.

The speed of sound is 343 m/s.

Compute the wavelength of the first mode of resonance.

Compute the wavelength of the second mode of resonance.

Compute the wavelength of the third mode of resonance.

Compute the frequency of the first mode of resonance.

Compute the frequency of the second mode of resonance.

Compute the frequency of the third mode of resonance.

Q2:

A sound wave of a frequency of 2.00 kHz is produced by a string oscillating in the mode. The linear mass density of the string is 0.0065 kg/m and the length of the string is 1.50 m. What is the tension in the string?

Q3:

A string has a linear mass density , a length , a tension of , and oscillates in a mode . What is the frequency of the oscillations?

Q4:

A nylon guitar string is fixed between two lab posts 2.00 m apart. The string has a linear mass density of and is placed under a tension of 160.00 N. The string is placed next to a tube, open at both ends, of length . The string is plucked and the tube resonates at the mode. The speed of sound is 343 m/s. What is the length of the tube?

Q5:

A string with a length of 4.0 m is held under a constant tension. The string has a linear mass density of 0.0060 kg/m. Two resonant frequencies of the string are 400 Hz and 480 Hz. There are no resonant frequencies between the two frequencies.

What is the wavelength of 400 Hz mode?

What is the wavelength of the 480 Hz mode?

What is the tension in the string?

Q6:

A string on the violin has a length of 23.0 cm and a mass of 0.900 grams. The tension in the string 850 N. The string is plucked and oscillates in the mode. The temperature in the room is .

What is the speed of the wave on the string?

What is the wavelength of the standing wave produced on the string?

What is the frequency of the oscillating string?

What is the frequency of the sound produced?

What is the wavelength of the sound produced?

Q7:

The column of air in a tube, which is closed at one end, has a fundamental frequency of 256 Hz. Some students fill the tube with water, and then slowly lower the water level by draining the tube. Whilst lowering the water level, the students repeatedly ring a 256-Hz tuning fork and listen for resonance with the air column. When the column of air reaches a length of 0.336 m, resonance first occurs.

What is the air temperature in the tube?

If the water level continues to lower, what length column of air will produce the second occurrence of resonance?

Q8:

What is the length of a tube that has a fundamental frequency of 176 Hz and a first overtone of 352 Hz if the speed of sound is 343 m/s?

Q9:

A 4.0-m-long tube, open at one end and closed at one end, is in a room where the temperature is . A speaker capable of producing variable frequencies is placed at the open end and is used to cause the tube to resonate.

What is the wavelength of the fundamental frequency of the tube?

What is the fundamental frequency of the tube?

What is the wavelength of the first overtone of the tube?

What is the frequency of the first overtone of the tube?

Q10:

A bassoon has a fundamental frequency of 90.0 Hz. It is open at both ends.

What is the frequency of the first overtone?

What is the frequency of the second overtone?

What is the frequency of the third overtone?