Exercises in HyperPhysics: Review of the physics of sound

The intent of these exercises is to show you a range of numerical answers associated with different physical phenomena; these are the type of calculations which are carried out in the problem-solving type physics courses. In the case of these exercises, the actual calculations are done by the computer but it is hoped that the exercises will help you become accustomed to the computer as a tool and a source of information.

A link to the Laboratory may be found in the right-hand column on the Physics 2030K Calendar, and the Laboratory list has a link to these exercises. Links in the exercises will take you to the calculation in HyperPhysics.

Note about entering numbers in calculations: When you enter a number in one of the calculations in HyperPhysics, you then just click anywhere outside the box to make sure the transaction is complete and the number is taken. If you need to edit the number, it is usually easiest to just double-click in the data entry box. That will turn the field dark, and any number you type will replace the previous number.

Exercise 1: Wave calculation

1. If a sound is produced at the orchestra standard frequency of 440 Hz, at a temperature where the speed of sound is 345 m/s, what is the wavelength of the sound produced?

2. If the limits of human hearing are 20 Hz to 20,000 Hz, what are the sound wavelengths associated with these extremes. You may use 345 m/s for the speed of sound.

3. What is the wavelength in meters of the electromagnetic carrier wave transmitted by the radio station WSB AM at 750 kHz? 1 kHz =103 Hz and the speed of light is 3 x 108 m/s.

4. What is the wavelength in meters of the electromagnetic carrier wave transmitted by GSU's WRAS at 88.5 MHz ? 1 MHz = 106 Hz.

Exercise 2: Open air column resonance
1. If a flute constitutes an open air column, how long must the air column be if it is to produce a frequency at middle-C, 261 Hz?

2. An open-ended organ pipe is to be constructed to sound the note A= 55 Hz, one octave above the bottom note on the piano. How long must the air column be?

3. If you open a hole on a recorder which is 20 cm from the edge (i.e., 0.2 meters is the length of the air column), what frequency should be produced?

Exercise 3: Closed air column resonance

1. A clarinet acts as a closed-ended air column. If its bottom note has a frequency of 148 Hz, how long is the column?

2. The ear canal responds most strongly to frequencies around 3700 Hz because that is the lowest resonant frequency of the canal. If the canal acts like a closed-ended cylinder, how long is the ear canal?

3. If the top resonance of the water tube resonance unit is at a column length of 8 cm when a tuning fork of frequency 1024 Hz , what is the corresponding speed of sound?

4. The lowest note on a local pipe organ is 16 Hz. Presuming that pipe to be a closed cylinder, what length must it have?

Exercise 4: Decibel calculation

1. If sound intensity IA is 100 times IB, then it is how many decibels more intense than IB?

2. If sound intensity IA is 2 times IB, then it is how many decibels more intense than IB?

3. If sound intensity IA is 4 times IB, then it is how many decibels more intense than IB?

4. If sound intensity IA is 1 dB more intense than IB, then IA is what multiple of IB?

Exercise 5: Inverse square law

1. If the front row of the auditorium is at 20 ft from the source and the sound level there is 90 dB, what will be the dB level at 40 ft from the source?

2. What will be the dB level at 200 ft from the source?

Exercise 6: Reverberation time

1. Suppose you had a room which was cube of dimension 10 meters with sound absorption coefficient a = 0.3. Find the reverberation time for this room.

2. Now if you took this same room and put acoustic tile with absorption coefficient a=0.9 on the ceiling, leaving all other parameters the same, what would be the reverberation time?

3. Now lower the ceiling to 5 meters and see what the reverberation time is.

4. Assuming a uniform absorption coefficient of 0.4, calculate the reverberation time of an auditorium of length 200 feet, width 100 ft and height 40 ft.

Exercise 7: Musical intervals in cents.

1. Taking the lowest note on the piano to be A0 at 27.5 Hz, what frequency is up by one equal tempered semitone (100 cents)?

2. Taking middle C to be 261.63 Hz, what is the frequency of the C-sharp, 100 cents up?

3. Calculate the frequency change to equal 5 cents at A-440 Hz.

4. Calculate the frequency change to equal 5 cents at the top end of the piano, 4186 Hz.

5. Starting at A-440Hz, calculate the frequency of a note which is an equal tempered fifth above it (700 cents). Then calculate the frequency of a note which is a just fifth above 440 Hz (702 cents).

6. Again starting at A-440Hz, calculate the frequency of a note which is an equal tempered major third above it (400 cents). Then calculate the frequency for a just major third above the 440 (386 cents).

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