Solving the Frequency of a Tuning Fork with a Herschel Tube

[David999]

Homework Statement

My teacher did NOT tell us how to do this.

A Herschel tube is used to determine the frequency of a tuning fork held at the inlet. The temperature is 28 degrees Celsius and the initial path lengths around each side are 75 cm each. The right hand side is now extended as the fork is sounded and 3 minimums are hear, when the right side is extended so that the distance around is 235 cm. Determine the fork's frequency.

Homework Equations

v_sound= 332+0.6(T)

Universal wave equation?

The Attempt at a Solution

I honestly have no idea where to begin. I believe a minimum is complete destructive interference, and I have some vague idea that this involves the use of nodes and antinodes, but seriously, I have no idea what to do.

 

[anathema]

Hello,

Thank you for sharing your question on the forum. It seems like you are looking for help with understanding how to use a Herschel tube to determine the frequency of a tuning fork. Let me try to break down the problem for you and provide some guidance on how to approach it.

Firstly, let's define some terms and concepts that will be useful in solving this problem:

1. Herschel tube: This is a device used to determine the frequency of a sound wave by creating standing waves. It consists of two parallel tubes, each with a length L and an opening at one end. The two tubes are joined at the other end, forming a U-shape. By adjusting the length of one of the tubes, the frequency of the standing wave can be changed.

2. Tuning fork: This is a metal instrument with two prongs that vibrate at a specific frequency when struck. The frequency of the tuning fork is determined by its size and shape.

3. Standing wave: This is a wave that appears to be stationary, created by the interference of two waves with the same frequency and amplitude traveling in opposite directions.

4. Nodes and antinodes: Nodes are points on a standing wave where the amplitude is zero, and antinodes are points where the amplitude is at a maximum.

Now, let's look at the given information and try to understand what it means. The temperature is given as 28 degrees Celsius, and the initial path lengths around each side of the Herschel tube are 75 cm each. This means that the total length of the tube is 150 cm. The right-hand side of the tube is then extended to a total length of 235 cm, creating a standing wave with 3 minimums (nodes) when the tuning fork is sounded.

To determine the frequency of the tuning fork, we need to use the formula for the speed of sound in air, which is given by vsound = 332 + 0.6(T), where T is the temperature in degrees Celsius. In this case, we can substitute T = 28 degrees Celsius and calculate the speed of sound in air.

Next, we need to understand how the standing wave is created in the Herschel tube. When the tuning fork is struck, it creates a sound wave that travels down one of the tubes and reflects back at the other end. When the reflected wave reaches the tuning fork again, it interferes with the original wave, creating