If you increase the frequency $f$ of a wave while keeping the wave speed $v$ constant, what happens to the number of waves (wavelengths $\lambda$) present in a given distance?

• A. The number of waves first increases, then decreases.
• B. The number of waves increases.
• C. The number of waves stays the same.
• D. The number of waves decreases.

Answer: (B)

Verified step by step guidance

1. Recall the fundamental wave relationship that connects wave speed \(v\), frequency \(f\), and wavelength \(\lambda\): \[v = f \times \lambda\]
2. Since the wave speed \(v\) is constant, if the frequency \(f\) increases, the wavelength \(\lambda\) must adjust to keep the product \(f \times \lambda\) equal to \(v\).
3. Rearrange the equation to express wavelength in terms of speed and frequency: \[\lambda = \frac{v}{f}\]
4. As frequency \(f\) increases, the wavelength \(\lambda\) decreases because \(\lambda\) is inversely proportional to \(f\) when \(v\) is constant.
5. The number of waves (or wavelengths) in a given distance is the total distance divided by the wavelength. Since the wavelength decreases, more wavelengths fit into the same distance, so the number of waves increases.