Ernst Mach lived in the late 19^{th} and early 20^{th} centuries and was a prominent Austrian physicist and philosopher of science. His studies of supersonic velocities, and the sound effects such motion produces, were published in 1877. He correctly described the effects observed when a projectile achieves supersonic speeds. For this reason, the speed of sound in air is named after him: ‘Mach 1’ means the speed of sound.

In this lab you will measure the speed of sound using the phenomenon of resonance. Resonance depends on the fact that objects have preferred frequencies at which they vibrate. Almost anything can be made to vibrate at any frequency but, depending on things like the length, mass and tension of an object, they have frequencies at which they will vibrate more strongly. The principle of resonance is why it is possible to hear the notes produced by the strings of violins and guitars and the resonant tubes of flutes and oboes. One interesting phenomenon is *harmonics* which reflects the fact that whole-number multiples and fractions of frequencies will also produce resonance with a given frequency.

You will use resonance at a length of ^{1}/_{4} wavelength to measure the speed of sound. You can do this because the velocity of a wave equals the wavelength times the frequency: ** v = λf** where

- water cylinder
- resonance tube
- tuning forks

- ruler
- lab notebook and pen
- vernier caliper

λ = 4 × [(0.4 × diam. of tube) + (h above water)]

- Fill the water cylinder completely full (to within 1 cm of the top) with the resonance tube in place.
- Record the frequency stamped on a tuning fork.
- Using a vernier caliper, record the inside diameter of the resonance tube.
- Strike the tuning fork on a book or the palm of your hand.
*Never strike the tuning fork on a hard surface such as the lab bench: it can be easily damaged.* - Pick up the top of the resonance tube and hold the vibrating tuning fork about 1 to 2 cm from the top of it. Raise the tube and fork until you locate the point of maximum amplitude (loudest volume). This may take a fair bit of trial and error to find the
*exact*height. - Use a ruler to measure the height of the top of the resonance tube above the surface of the water.
- Repeat steps 2 through 6 for three other tuning forks.

- Use the formula from the mathematical toolkit to find the length of
^{1}/_{4}wavelength for each tuning fork: add the distance of 0.4 × the diameter of the resonance tube to the height you measured in step 6. - Multiply the length you find (be careful with units!) by four to get the full wavelength.
- Calculate the experimental speed of sound (Mach 1) for each tuning fork. Find the average velocity.
- Calculate the theoretical speed of sound using the velocity formula from the mathematical toolkit (T
_{c}is the room temperature in °C). Use this to find the percent error, using the average you found. - What are some common errors in this experiment?
- You probably found some fairly wide variation in speeds for the various tuning forks. Explain why they should, in theory, all give the same speed for the sound.
- Which wavelengths gave results for the speed of sound that had high percent errors? To what do you attribute this pattern (if any)?
- If the British Airways Concorde jet were still in operation, and flew between Portland, Maine and New York City (500 km), how long would it take (in minutes) to fly that route at Mach 1.5? How long would it take at highway speeds of 30 m/s?
- When sound enters another medium, such as the wall or a swimming pool, what remains constant?
- If sound travels at 1,500 m/s in distilled water, calculate the wavelength for each of your tuning forks in a beaker of distilled water.

An *individual* informal report showing a data table and the answers to the questions in the Analysis section.