The larger the frequency of the tuning fork,

the smaller the length of the tube at which you hear the resonant sound.
Explain why this is so (think in terms of the relationship between frequency and wavelength).

Wavelength = V/F.

V = The speed of light.
F = Frequency.

The wavelength is inversely proportional to the frequency. In other words, if the frequency is doubled; the wavelength is cut in half.

the larger the fork the smaller the frequency

To understand why the length of the tube at which resonant sound is heard decreases as the frequency of the tuning fork increases, we need to consider the relationship between frequency and wavelength.

In a tube, the resonant sound occurs when the length of the tube matches an integral multiple of half-wavelengths of the sound wave. This phenomenon is known as standing waves.

Now, let's think about the relationship between frequency and wavelength. The wavelength (λ) is inversely proportional to the frequency (f) of a sound wave. Mathematically, we can represent this relationship as:

λ = v / f

Where:
λ = Wavelength
v = Velocity of sound in the medium
f = Frequency

Since the speed of sound in a given medium remains constant, we can simplify the equation to:

λ ∝ 1 / f

Now, when we consider a tuning fork with a higher frequency, its wavelength becomes smaller. This means that for a given length of the tube, the number of half-wavelengths that can fit inside it increases as the wavelength decreases.

When the length of the tube is such that it matches an integral multiple of half-wavelengths of the sound wave, a standing wave is formed, leading to resonance and amplification of the sound. As the frequency increases and the wavelength decreases, the number of half-wavelengths that can fit into the tube increases. Consequently, the length of the tube required for resonance decreases.

In summary, the relationship between frequency and wavelength determines the resonant length of the tube. As the frequency increases, the wavelength decreases, and more half-wavelengths can fit into a given length of the tube, resulting in a smaller resonant length.