Question

Sound waves propagates with a speed of \(350 \mathrm{~m} / \mathrm{s}\) through air and with a speed of \(3500 \mathrm{~m} / \mathrm{s}\) through brass. If a sound wave having frequency \(700 \mathrm{~Hz}\) passes from air to brass, then its wavelength ......... (A) decreases by a fraction of 10 (B) increases 20 times (C) increases 10 times (D) decreases by a fraction of 20

Short answer

The wavelength of the sound wave increases 10 times as it passes from air to brass.

Step-by-step solution

Determine the wavelength in air

According to the exercise, the speed of sound in air is 350 m/s, and the frequency of the sound wave is 700 Hz. We'll start by finding the wavelength in air using the formula: Wave speed = Frequency × Wavelength \(350 = 700 \times \lambda_\mathrm{air}\) Divide both sides by 700 to find the wavelength in air: \(\lambda_\mathrm{air} = \frac{350}{700}\) \(\lambda_\mathrm{air} = 0.5 \mathrm{~m}\)

Determine the wavelength in brass

Now we'll find the wavelength in brass, using the same formula. The speed of sound in brass is 3500 m/s, and the frequency remains the same at 700 Hz: \(3500 = 700 \times \lambda_\mathrm{brass}\) Divide both sides by 700 to find the wavelength in brass: \(\lambda_\mathrm{brass} = \frac{3500}{700}\) \(\lambda_\mathrm{brass} = 5 \mathrm{~m}\)

Determine the change in wavelength

Now that we've found the wavelengths in air and brass, we can determine the change in wavelength: \(\frac{\lambda_\mathrm{brass}}{\lambda_\mathrm{air}} = \frac{5}{0.5}\) This simplifies to: \(\frac{\lambda_\mathrm{brass}}{\lambda_\mathrm{air}} = 10\) So, the wavelength in brass increases 10 times compared to the wavelength in air.

Match the result with answer choices

Now, we match our result with the answer choices provided. The wavelength increases 10 times, which matches with answer choice (C). Therefore, the correct answer is: (C) increases 10 times