Lucy has three sources of sound that produce pure tones with wavelengths of 60 cm, 100 cm, and 124 cm. She also has an assortment of narrow tubes that are closed at one end and open at the other. After experimenting, Lucy notices that each tone will resonate with tubes of some lengths but not with others.

For each wavelength, determine which tube lengths, if any, will resonate with the sound of that wavelength.

a. 60 cm, 100 cm, and 124 cm
b. 30 cm, 50 cm, and 62 cm
c. 120 cm, 200 cm, and 248 cm
d. 90 cm, 150 cm, and 186 cm

Tubes with lengths of 80 cm, 133.33 cm, and 165.33 cm will resonate with sound wavelengths of 60 cm, 100 cm, and 124 cm respectively. Therefore the correct option is A

Explanation:

When sound waves resonate in a tube closed at one end, the wavelength of the sound is related to the length of the tube. For a tube closed at one end, the standing wave inside the tube has three-fourths of its wavelength in the tube, or λ' = 4L/3. This means that tubes with lengths equal to 4 times the wavelength divided by 3 will resonate with the sound.

Therefore, for the given wavelengths of 60 cm, 100 cm, and 124 cm, the corresponding tube lengths that will resonate with the sound are:

A tube length of 4 times 60 cm divided by 3, which is 80 cm
A tube length of 4 times 100 cm divided by 3, which is approximately 133.33 cm
A tube length of 4 times 124 cm divided by 3, which is approximately 165.33 cm