In this sound interferometer, sound waves enter at A and travel to C via paths ABC and ADC. the intensity of the sound can be determined by the microphone placed at C. The length of the path ADC can be changed by a sliding tube.

The frequency is fixed at a certain value and the tube is filled with oxygen gas. Successive minima are detected each time the distance ADC is increased by 0.03m. when the experiment is repeated using hydrogen gas, the corresponding change in ADC is 1.2m.
If the speed of sound in oxygen is 320m/s, would sound move faster or slower in hydrogen?

To determine whether sound would move faster or slower in hydrogen compared to oxygen, we can use the formula for the speed of sound:

Speed of sound (v) = Frequency (f) x Wavelength (λ)

Since the frequency is fixed, we can rearrange the formula to solve for the wavelength:

Wavelength (λ) = Speed of sound (v) / Frequency (f)

Let's calculate the wavelength of sound in oxygen first:

Wavelength in oxygen (λ_oxygen) = Speed of sound in oxygen (v_oxygen) / Frequency (f)

Given that the speed of sound in oxygen is 320 m/s, we need to determine the frequency in order to calculate the wavelength. If you have the frequency, substitute it into the equation above to obtain the wavelength in oxygen.

Next, we can calculate the wavelength of sound in hydrogen:

Wavelength in hydrogen (λ_hydrogen) = Speed of sound in hydrogen (v_hydrogen) / Frequency (f)

Given that the change in length of ADC is 1.2 m when the experiment is repeated using hydrogen gas, this corresponds to a change in wavelength. Since the frequency remains constant, we can calculate the wavelength in hydrogen using the value for the change in ADC.

Now, comparing the wavelengths in oxygen and hydrogen, we can determine whether sound would move faster or slower in hydrogen. If the wavelength in hydrogen is shorter than the wavelength in oxygen, then sound would move faster in hydrogen. Conversely, if the wavelength in hydrogen is longer, sound would move slower in hydrogen.

By calculating the wavelengths in both gases using the provided information, we can determine the relative speeds of sound in oxygen and hydrogen and answer the question.