A string fixed at both ends and having a mass of 3.10 g, a length of 3.90 m and a tension of 40.0 N vibrates in its second (n = 2) normal mode. (Assume the speed of sound in air is 343 m/s.) %3D (a) Is the wavelength in air of the sound emitted by this vibrating string larger or smaller than the wavelength of the wave on the string?

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### Physics Problem: Vibrating String and Sound Wavelength

**Problem Statement:**
A string fixed at both ends and having a mass of 3.10 g, a length of 3.90 m, and a tension of 40.0 N vibrates in its second \((n = 2)\) normal mode. (Assume the speed of sound in air is 343 m/s.)

**Questions:**

(a) Is the wavelength in air of the sound emitted by this vibrating string larger or smaller than the wavelength of the wave on the string?
- larger
- smaller
- There is not enough information.

(b) What is the ratio of the wavelength in air of the sound emitted by this vibrating string and the wavelength of the wave on the string?

\[
\frac{\lambda_{\text{air}}}{\lambda_{\text{string}}} = \ \_\_\_\_\_\_\_\_\_
\]

**Note:** Select the appropriate response and provide the needed ratio to complete the problem.

### Additional Information:
- The mass of the string is 3.10 g.
- The length of the string is 3.90 m.
- The tension in the string is 40.0 N.
- The string vibrates in its second normal mode.

### Supporting Tools:
- A “Need Help?” section with a "Read It" button for additional assistance.
- Submission feature for answers.

**User Interface:**
- A section to input answers.
- Navigation tools at the bottom to view saved work or revert to the last response.
Transcribed Image Text:### Physics Problem: Vibrating String and Sound Wavelength **Problem Statement:** A string fixed at both ends and having a mass of 3.10 g, a length of 3.90 m, and a tension of 40.0 N vibrates in its second \((n = 2)\) normal mode. (Assume the speed of sound in air is 343 m/s.) **Questions:** (a) Is the wavelength in air of the sound emitted by this vibrating string larger or smaller than the wavelength of the wave on the string? - larger - smaller - There is not enough information. (b) What is the ratio of the wavelength in air of the sound emitted by this vibrating string and the wavelength of the wave on the string? \[ \frac{\lambda_{\text{air}}}{\lambda_{\text{string}}} = \ \_\_\_\_\_\_\_\_\_ \] **Note:** Select the appropriate response and provide the needed ratio to complete the problem. ### Additional Information: - The mass of the string is 3.10 g. - The length of the string is 3.90 m. - The tension in the string is 40.0 N. - The string vibrates in its second normal mode. ### Supporting Tools: - A “Need Help?” section with a "Read It" button for additional assistance. - Submission feature for answers. **User Interface:** - A section to input answers. - Navigation tools at the bottom to view saved work or revert to the last response.
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