In Quincke's experiment the sound detected is changed from a maximum to a minimum when the sliding tube is moved through a distance of 2.50 cm. Find the frequency of sound if the speed of sound in air is `340 m s^-1`.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the relationship between distance moved and wavelength
In Quincke's experiment, the sound detected changes from maximum (antinode) to minimum (node) when the sliding tube is moved through a distance of 2.50 cm. This distance corresponds to a quarter of the wavelength (λ/4) because the transition from an antinode to a node represents a quarter of the wavelength.

### Step 2: Set up the equation for the distance moved
Given that the distance moved is 2.50 cm, we can express this in meters:
\[ d = 2.50 \, \text{cm} = 0.025 \, \text{m} \]

Since this distance corresponds to λ/4, we can write:
\[ \frac{\lambda}{4} = 0.025 \, \text{m} \]

### Step 3: Solve for the wavelength (λ)
To find the wavelength (λ), we multiply both sides of the equation by 4:
\[ \lambda = 4 \times 0.025 \, \text{m} = 0.1 \, \text{m} \]

### Step 4: Use the speed of sound to find the frequency
The speed of sound (v) in air is given as 340 m/s. The relationship between speed (v), frequency (ν), and wavelength (λ) is given by the equation:
\[ v = \lambda \cdot \nu \]
Rearranging this equation to solve for frequency (ν), we get:
\[ \nu = \frac{v}{\lambda} \]

### Step 5: Substitute the known values
Substituting the values we have:
\[ \nu = \frac{340 \, \text{m/s}}{0.1 \, \text{m}} \]

### Step 6: Calculate the frequency
Now, performing the calculation:
\[ \nu = 3400 \, \text{Hz} \]
This can also be expressed in kilohertz (kHz):
\[ \nu = 3.4 \, \text{kHz} \]

### Final Answer
The frequency of the sound is **3400 Hz** or **3.4 kHz**.

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