In this example, sound waves are created in a tube. The tube is partially filled with water and the level of water is adjusted in the tube until there is a standing wave. Draw the lowest frequency standing wave for the two water levels in the drawing. The drawing has two tubes. One is 3/4 full and the other is 1/4 of the way full.
A 320 Hz tuning fork to generate sound waves. The tube has a length of 1m. Taking the speed of sound to be 343 m/s, find the two heights of the water int the tube that will produce a standing wave.
To draw the lowest frequency standing wave for the two water levels in the tube, we first need to understand the concept of standing waves in tubes. In a tube partially filled with water, sound waves can create standing waves when the length of the tube matches certain multiples of the wavelength of the sound waves.
In the case of a tube with one end open (as in this example), the lowest frequency (also known as the fundamental frequency) occurs when the length of the tube is equal to a quarter of the wavelength of the sound wave. When the tube is partially filled with water, we adjust the water level until a standing wave is formed.
Let's start by finding the wavelength of the sound wave generated by the 320 Hz tuning fork. The speed of sound is given as 343 m/s, and the frequency of the tuning fork is 320 Hz. We can use the formula:
wavelength = speed of sound / frequency
wavelength = 343 m/s / 320 Hz = 1.07125 m
Now, let's consider the tube that is 3/4 full:
To form a standing wave with the lowest frequency, we need the length of the tube to be one-quarter of the wavelength. Since the tube has a length of 1m, we can calculate the required water level by multiplying 1/4 by the wavelength:
water level = (1/4) * 1.07125 m = 0.2678 m
Therefore, the water level in the tube that will produce a standing wave with the lowest frequency is approximately 0.268 m.
Now, let's consider the tube that is 1/4 full:
Similarly, for the tube to form a standing wave with the lowest frequency, we need the length of the tube to be one-quarter of the wavelength. Again, since the tube has a length of 1m, we can calculate the required water level by multiplying 1/4 by the wavelength:
water level = (1/4) * 1.07125 m = 0.2678 m
Therefore, the water level in the tube that will produce a standing wave with the lowest frequency is approximately 0.268 m.
To summarize, the water levels in the tube that will produce a standing wave with the lowest frequency are approximately 0.268 m for both the tube that is 3/4 full and the tube that is 1/4 full.