Question:

A tuning fork with a frequency of 440 Hz is struck and held above the open end of a vertical, capped tube. The tube is slowly raised and lowered in a water-filled container, while a microphone is placed just above the tube opening to record the sound produced. The graph below shows the intensity of the recorded sound as a function of the tube height above the water level.

(a) Explain the observed pattern in the graph.

(b) Calculate the speed of sound in air at the temperature and atmospheric conditions present during the experiment.

(c) If the temperature of the room increases while the experiment is being conducted, what effect would this have on the recorded sound intensity graph? Provide a qualitative explanation.

Answer:

(a) The observed pattern in the graph can be explained by the principles of resonance. When the tuning fork is held above the open end of the tube, sound waves are produced and a stationary wave is set up within the tube. At certain tube heights, the stationary wave is in resonance, resulting in an increased amplitude and thus a higher intensity of the recorded sound. These tube heights correspond to the wavelengths that produce constructive interference, maximizing the sound intensity. Consequently, the graph displays peaks where the tube height corresponds to the resonant wavelengths, and valleys between the peaks where the tube height corresponds to the nodes of the stationary wave.

(b) To calculate the speed of sound in air, we can use the formula:

v = fλ

Where: v = speed of sound (m/s) f = frequency of the tuning fork (Hz) λ = wavelength of the sound wave (m)

From the graph, we can determine the wavelengths of the resonant sound waves by measuring the distances between consecutive peaks or valleys. Let's assume the distance between two consecutive peaks (or valleys) is given by λ/2.

From the graph, it can be observed that the distance between two consecutive peaks (or valleys) is approximately 1.4 cm. Therefore, λ/2 = 1.4 cm = 0.014 m

We know the frequency of the tuning fork is 440 Hz.

Hence, the speed of sound in air can be calculated as follows:

v = fλ = 440 Hz × 0.014 m = 6.16 m/s

Therefore, the speed of sound in air during the experiment is approximately 6.16 m/s.

(c) If the temperature of the room increases while the experiment is being conducted, the speed of sound in air would increase. This is because the speed of sound is directly proportional to the square root of the temperature. As the temperature increases, the molecules in the air gain more kinetic energy, resulting in an increase in their average speed. Consequently, the sound waves traveling through the air will propagate faster, leading to an increase in the speed of sound. This would affect the recorded sound intensity graph by shifting the resonant tube heights to slightly higher positions along the y-axis, resulting in a compressed pattern on the graph. In other words, the graph would shift upward, with the peaks occurring at slightly higher tube heights and the valleys occurring at slightly higher positions as well.