Physics 1001: Laboratory 3.

Standing Waves.

Your name/student number:_________________________________

Date:_________ Marker’s signature:______________ Mark:______

Pre-lab Question 1:

What is the wavelength of a sound wave of frequency 500 Hz in air (you will need to look up the speed of sound in air)? ________ m.

Pre-lab Question 2:

If a person inhales helium gas the sound of their voice changes quite dramatically. Why?

Pre-lab Question 3:

A shower cubicle measures 0.86x0.86x2.1 m. If you were to sing in this shower what frequencies will be amplified? (The amplified frequencies will correspond to the resonant frequencies of the cubicle, assume it acts like a pipe closed at both ends so there must be a node at both ends. Take the range of the human voice to be 130 to 2000 Hz.)

Part 1. Resonant frequencies of open and closed pipes.

Following the instructions in the lab measure the resonant frequencies of the tube open at both ends. You may not be able to fill all the spaces in the table, but should find at least five resonant frequencies. The frequency difference column should be filled with the differences between the resonant frequency you have just measured and the next lower resonant frequency.

Open tube resonant frequencies.

Divisions

Time / Division

Period (T)

Frequency (1 / T)

Frequency difference

By considering the differences between the resonant frequencies, construct a linear equation describing the resonant frequencies.

______________________________.

Again following the directions in the lab manual close one end of the tube and measure the resonant frequencies.

Closed tube resonant frequencies.

Divisions

Time / Division

Period (T)

Frequency (1 / T)

Frequency Difference

As you did for the open tube, construct a linear equation describing the resonant frequencies of the closed tube.

______________________________.

Compare the equations you have determined for the open and closed tubes. What differences do you notice?

The resonant wavelengths are determined by the length of the tube, if it is open λ = 2 Lopen (n+1)-1 or if it is closed λ = 4 Lclosed (2n+1)-1 in both cases taking the fundamental as n=0. Being careful of what value you use for n, work out the wavelengths of the resonant modes you have observed and thus the speed of sound from each observation.

Table of the measured sound velocities.

Open Tube

Frequency

Wavelength

Velocity

Closed Tube

Frequency

Wavelength

Velocity

What is your average speed of sound, and how does it compare to the standard value of 340 m s-1?

What are some of the factors that could cause the speed to be different to the standard value?

Part 2. Geometry of standing waves.

Choose the resonant frequency for the open tube closest to 600 Hz and measure the positions of the extrema of the standing wave using the microphone.

Positions of maxima and minima of the standing wave in an open tube. Frequency

Max 1

Min 1

Max 2

Min 2

Max 3

Min 3

Max 4

Min 4

Repeat the measurement of one of these positions five times as described in the lab manual. Extremum

1

2

3

4

5

Since they are being measured with a microphone the positions found are extrema of the pressure in the tube. Is the pressure wave you have just measured in phase or out of phase with the displacement wave usually described when discussing waves? (Have a look at figure 4 in the lab manual, and the accompanying explanation for a hint.)

Make a sketch of what is going on inside the tube, including both pressure and displacement waves.

Reconstruct the closed tube and repeat your measurements of the positions of the maxima and minima of the resonant mode with frequency nearest to 600 Hz.

Positions of maxima and minima of the standing wave in a closed tube. Frequency

Max 1

Min 1

Max 2

Min 2

Max 3

Min 3

Max 4

Min 4

Make another sketch of what...