Question

Sound waves travel at \(350\) m/s through a warm air and at \(3500\) m/s through brass. Which of the following is correct about the wavelength of a \(700\) Hz accoustic wave as it enters brass from warm air?

• A. It increase by a factor \(20\)
• B. It decrease by a factor \(10\)
• C. It increase by a factor \(10\)
• D. It decrease by a factor \(20\)

Hint:

Frequency stays fixed while the speed changes, so \(\lambda = v/f\) scales with speed.

Answer 1

The Correct Option is C

Step 1: Plan:
Use the ratio of speeds, since $f$ is the same.

Step 2: Steps:
$\frac{\lambda_{\text{brass}}}{\lambda_{\text{air}}} = \frac{v_{\text{brass}}}{v_{\text{air}}} = \frac{3500}{350} = 10$. Faster speed means longer wavelength, so it increases $10$ times. A drop by $10$ or $20$ times would need a slower medium.

Final Answer:
The wavelength increases by a factor of $10$, option (C). \[ \boxed{\text{Increases by a factor of 10}} \]