The table below shows the speed of sound waves from musical sound sources at 20°C.

Which conclusion can be made based on the information in the table?

Wave speed and wavelengths can vary inversely to produce the same frequency.
Frequency and wave speed can vary directly to produce the same wavelength.
Wavelengths and frequency can vary inversely to produce the same wave speed.
Frequency and wavelengths can vary directly to produce the same wave speed.

1 answer

To analyze the relationships between wave speed (v), frequency (f), and wavelength (λ), we can use the fundamental equation of wave motion:

\[ v = f \times \lambda \]

From this equation, we can derive the following relationships:

  1. Wave speed (v) and wavelength (λ) can vary inversely to produce the same frequency (f): If frequency is constant and wavelength increases, wave speed must also increase, and vice versa.

  2. Frequency (f) and wave speed (v) can vary directly with the same wavelength (λ): If the wavelength is constant, any increase in wave speed results in a proportional increase in frequency.

  3. Wavelength (λ) and frequency (f) can vary inversely to produce the same wave speed (v): If wave speed is constant, an increase in frequency means the wavelength must decrease, and vice versa.

  4. Frequency (f) and wavelengths (λ) can vary directly to produce the same wave speed (v): This statement is incorrect because if wave speed is constant, an increase in frequency results in a decrease in wavelength.

Given these relationships, the correct conclusion based on the information in the table is:

Wavelengths and frequency can vary inversely to produce the same wave speed.

So, the statement that aligns with our derived relationships is: Wavelengths and frequency can vary inversely to produce the same wave speed.