To determine the frequency of the tuning fork, we use the wave equation:

$v = f \lambda$

where:

• $v$ is the speed of sound ($345.0$ m/s),
• $f$ is the frequency of the wave (which we need to find),
• $\lambda$ is the wavelength ($0.62$ m).

Step 1: Solve for Frequency

Rearrange the equation to solve for $f$:

$f = \frac{v}{\lambda}$

Substituting the given values:

$f = \frac{345.0 \text{ m/s}}{0.62 \text{ m}}$

$f = 556.45 \text{ Hz}$

Final Answer:

$\boxed{556.45 \text{ Hz}}$

This means the tuning fork vibrates at approximately 556.45 Hz, producing sound at this frequency.

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Do you need further explanation or details on the calculation?

Here are five related questions to expand on this concept:

1. How does temperature affect the speed of sound?
2. What is the relationship between frequency and pitch in sound waves?
3. How would the frequency change if the wavelength were doubled?
4. What is the second resonance wavelength for this tuning fork?
5. How does the medium (air, water, metal) affect the speed of sound?

Tip:

The speed of sound increases with temperature because warmer air has more energetic molecules, allowing sound waves to propagate faster.