A vertical tube is made to stand in water so that the water level can be adjusted. Sound wave of frequency `320Hz` are sent into the top of the tube. If standing waves are produced at two successive water levels of `20 cm` and `73 cm`, what is the speed of sound waves in the air in the tube (in `m//s`)

Options

A. `339`
B. `332`
C. `334`
D. `336`

Explanation

To find the speed of sound waves in the air in the tube, we can follow these steps:

### Step 1: Identify the given values
- Frequency of the sound wave, \( f = 320 \, \text{Hz} \)
- Water level heights:
- First level, \( L_1 = 20 \, \text{cm} = 0.20 \, \text{m} \)
- Second level, \( L_2 = 73 \, \text{cm} = 0.73 \, \text{m} \)

### Step 2: Calculate the difference in lengths
- The difference in lengths of the two water levels:
\[ \Delta L = L_2 - L_1 = 0.73 \, \text{m} - 0.20 \, \text{m} = 0.53 \, \text{m} \]

### Step 3: Use the formula for the speed of sound in a tube
In a tube with standing waves, the speed of sound \( V \) can be calculated using the formula:
\[ V = 2f \Delta L \]
Where:
- \( f \) is the frequency
- \( \Delta L \) is the difference in lengths of the water levels

### Step 4: Substitute the values into the formula
Substituting the known values into the formula:
\[ V = 2 \times 320 \, \text{Hz} \times 0.53 \, \text{m} \]

### Step 5: Calculate the speed of sound
Now, perform the calculation:
\[ V = 2 \times 320 \times 0.53 = 339.2 \, \text{m/s} \]

### Step 6: Round the result
Rounding to the nearest whole number, we get:
\[ V \approx 339 \, \text{m/s} \]

### Final Answer
The speed of sound waves in the air in the tube is approximately \( 339 \, \text{m/s} \).

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