Question

tuesday
instructions: for each problem below that requires an equation, show your work and include your answer with the correct units.

scenario 1
two physics students are doing an experiment. they are trying to measure the speed of sound waves. one sounds a horn from one end of the football field. the other student who is 1029 meters away hears it after 3 seconds.

1. was it a longitudinal or transverse wave?
2. how fast did the sound travel?
3. if the frequency of the horn was 420 hz, what was the wavelength?
4. if they want to produce a sound with a longer wavelength, they need to get a horn with a different frequency. do they want a lower or higher frequency? why? (hint: think about the velocity equation)

scenario 2
to play \mary had a little lamb\ on the piano, you only need three notes.

1. the first note has a wavelength of 1.04 meters. if we played it at room temperature (where the speed of sound is 343 m/s), what is the frequency of the first note?
2. using the chart above, find the identity of the first note by matching its frequency to the frequency you calculated in the previous question.

Explanation:

Step1: Identify wave type

Sound waves are longitudinal because they propagate by compressing and rarefacting the medium (air) parallel to the direction of wave travel.

Step2: Calculate sound speed

Use speed formula $v=\frac{d}{t}$
$v=\frac{1029\ \text{m}}{3\ \text{s}}=343\ \text{m/s}$

Step3: Calculate wavelength

Use wave equation $\lambda=\frac{v}{f}$
$\lambda=\frac{343\ \text{m/s}}{420\ \text{Hz}}\approx0.82\ \text{m}$

Step4: Relate wavelength and frequency

From $v=f\lambda$, at constant $v$, $\lambda\propto\frac{1}{f}$. Longer wavelength needs lower frequency.

Step5: Calculate note frequency

Use $f=\frac{v}{\lambda}$
$f=\frac{343\ \text{m/s}}{1.04\ \text{m}}\approx329.81\ \text{Hz}$

Step6: Match frequency to note

The calculated frequency matches the frequency of E4 (329.63 Hz, close to 329.81 Hz).

Answer:

1. Longitudinal wave
2. $343\ \text{m/s}$
3. $0.82\ \text{m}$
4. Lower frequency; because at constant wave speed, wavelength and frequency are inversely proportional, so a longer wavelength requires a smaller frequency.
5. $329.81\ \text{Hz}$
6. E4