Understanding the Relationship: Sound Frequency, Wavelength, and Speed

The question asks about the fundamental relationship connecting the frequency, wavelength, and speed of a sound wave. This relationship is a core concept in wave physics and applies to all types of waves, including sound waves.

Let's define the terms involved:

• Speed (v): This is how fast the wave travels through the medium. For sound, this is the speed of sound. It is typically measured in meters per second (m/s).
• Frequency (f): This is the number of wave cycles that pass a point in one second. It tells us how often a part of the wave oscillates. It is measured in Hertz (Hz), which is equivalent to cycles per second ($s^{-1}$).
• Wavelength ($\lambda$): This is the distance between two consecutive identical points on a wave, such as peak to peak or trough to trough. It is the spatial length of one complete cycle. It is measured in meters (m).

The relationship between these three quantities for any wave is given by the wave equation:

\begin{equation*} v = f\lambda \end{equation*}

This equation states that the speed of the wave is equal to the product of its frequency and its wavelength.

The question asks for the relation when solving for the frequency (f). We can rearrange the wave equation ($v = f\lambda$) to isolate f:

Divide both sides of the equation by $\lambda$:

\begin{equation*} \frac{v}{\lambda} = \frac{f\lambda}{\lambda} \end{equation*}

This simplifies to:

\begin{equation*} f = \frac{v}{\lambda} \end{equation*}

This shows that the frequency of a wave is equal to its speed divided by its wavelength.

Let's look at the given options:

1. f = v/λ
2. f = λ v
3. f = λ/v
4. f = λv ²

Comparing our derived relationship ($f = v/\lambda$) with the options, we see that option 1 matches the correct relation.

Here is a summary of the variables and their standard units:

Revision Table: Sound Wave Relationship

Understanding the formula $v = f\lambda$ is crucial for solving problems involving sound waves and other types of waves. Remember that while frequency and wavelength can change when a wave moves from one medium to another, the frequency usually remains constant (determined by the source), and the speed and wavelength adjust accordingly.

Additional Information: Properties of Sound Waves

Sound waves are longitudinal waves, meaning the particles of the medium vibrate parallel to the direction of energy transfer. The speed of sound depends on the properties of the medium it travels through, such as its density and compressibility. For example, sound travels faster in solids than in liquids, and faster in liquids than in gases. Temperature also affects the speed of sound in a gas; the speed increases with increasing temperature.