The speed of sound waves in air is 340 m/s and 5600 m/s through steel. The wavelength of a 1000 Hz acoustic wave travelling from air to steel will

Options

A. decrease by a factor 15
B. increase by a factor 20
C. decrease by a factor 10
D. increase by a factor 16.5

Explanation

To find the wavelength of a 1000 Hz acoustic wave traveling from air to steel, we can follow these steps:

### Step 1: Understand the relationship between speed, frequency, and wavelength
The relationship between speed (V), frequency (f), and wavelength (λ) is given by the formula:
\[ V = f \times \lambda \]
Where:
- \( V \) is the speed of sound in the medium,
- \( f \) is the frequency of the wave,
- \( \lambda \) is the wavelength of the wave.

### Step 2: Identify the given values
From the problem, we have:
- Speed of sound in air, \( V_A = 340 \, \text{m/s} \)
- Speed of sound in steel, \( V_S = 5600 \, \text{m/s} \)
- Frequency of the wave, \( f = 1000 \, \text{Hz} \)

### Step 3: Calculate the wavelength in air
Using the formula \( V = f \times \lambda \), we can rearrange it to find the wavelength in air (\( \lambda_A \)):
\[ \lambda_A = \frac{V_A}{f} \]
Substituting the known values:
\[ \lambda_A = \frac{340 \, \text{m/s}}{1000 \, \text{Hz}} = 0.34 \, \text{m} \]

### Step 4: Calculate the wavelength in steel
Now, we can find the wavelength in steel (\( \lambda_S \)) using the same formula:
\[ \lambda_S = \frac{V_S}{f} \]
Substituting the known values:
\[ \lambda_S = \frac{5600 \, \text{m/s}}{1000 \, \text{Hz}} = 5.6 \, \text{m} \]

### Step 5: Compare the wavelengths
We can now compare the wavelengths in air and steel. The wavelength in steel is significantly larger than that in air.

### Conclusion
The wavelength of the 1000 Hz acoustic wave traveling from air to steel is \( \lambda_S = 5.6 \, \text{m} \).

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