A violin string 15.0 cm long and fixed at both ends oscillates in its N = 1 mode. The speed of waves on the string is 280 m/s, and the speed of sound in air is 318 m/s. What are the (a) frequency and (b) wavelength of the emitted sound wave?

Explanation

To solve the problem step by step, we need to find the frequency and wavelength of the emitted sound wave from a violin string that is oscillating in its fundamental mode (N = 1).

### Step 1: Determine the Wavelength of the String Vibration

The length of the violin string is given as \( L = 15.0 \, \text{cm} = 0.15 \, \text{m} \).

In the fundamental mode (N = 1), the relationship between the wavelength (\( \lambda \)) and the length of the string is given by:

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