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: Understanding the Concept:
When a wave goes from one medium to another, its frequency stays the same. The speed and the wavelength change, with \(\lambda = \frac{v}{f}\).

Step 2: Calculate:
In air: \(\lambda_1 = \frac{350}{700} = 0.5\) m. In brass: \(\lambda_2 = \frac{3500}{700} = 5\) m.
\(\frac{\lambda_2}{\lambda_1} = 10\), so the wavelength increases by a factor of \(10\).

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