Sounds waves travel at `350m//s` through a warm air and at `3500m//s` through brass. The wavelength of a `700 Hz`. Acoustic wave as it enters brass from warm air

Options

A. decreases by a factor 10
B. increases by a factor 10
C. increases by a factor 10
D. decreases by a factor 20

Explanation

To find the wavelength of a 700 Hz acoustic wave as it enters brass from warm air, we can follow these steps:

### Step 1: Understand the relationship between speed, frequency, and wavelength
The fundamental relationship for waves is given by the equation:
\[ V = f \cdot \lambda \]
where:
- \( V \) is the speed of the wave,
- \( f \) is the frequency,
- \( \lambda \) is the wavelength.

### Step 2: Identify the given values
From the question, we have:
- Speed of sound in warm air, \( V_1 = 350 \, \text{m/s} \)
- Speed of sound in brass, \( V_2 = 3500 \, \text{m/s} \)
- Frequency of the wave, \( f = 700 \, \text{Hz} \)

### Step 3: Calculate the wavelength in warm air
Using the wave equation for warm air:
\[ V_1 = f \cdot \lambda_1 \]
Substituting the known values:
\[ 350 = 700 \cdot \lambda_1 \]
To find \( \lambda_1 \):
\[ \lambda_1 = \frac{350}{700} = 0.5 \, \text{m} \]

### Step 4: Calculate the wavelength in brass
Now, using the wave equation for brass:
\[ V_2 = f \cdot \lambda_2 \]
Substituting the known values:
\[ 3500 = 700 \cdot \lambda_2 \]
To find \( \lambda_2 \):
\[ \lambda_2 = \frac{3500}{700} = 5 \, \text{m} \]

### Step 5: Determine the change in wavelength
Now we compare \( \lambda_2 \) with \( \lambda_1 \):
- \( \lambda_1 = 0.5 \, \text{m} \)
- \( \lambda_2 = 5 \, \text{m} \)

To find the factor by which the wavelength increases:
\[ \text{Factor} = \frac{\lambda_2}{\lambda_1} = \frac{5}{0.5} = 10 \]

### Conclusion
The wavelength of the 700 Hz acoustic wave increases by a factor of 10 as it enters brass from warm air.