Wave problems 1 and 2

Wave questions I

1.  Differentiate between mechanical and electromagnetic waves.  Give examples.

2.  Draw a wave and identify the primary parts (wavelength, crest, trough, amplitude).

3.  Find the speed of a 500 Hz wave with a wavelength of 0.4 m.

4.  What is the frequency of a wave that travels at 24 m/s, if 3 full waves fit in a 12-m space?  (Hint:  find the wavelength first.)

5.  Approximately how much greater is the speed of light than the speed of sound?

6.  Harmonics

a.  Draw the first 3 harmonics for a wave on a string.
b.  If the frequency of the first harmonic (n = 1) is 10 Hz, find the frequencies of the next 2 harmonics.
c.  What is true about the speeds of the harmonics?

7.  Show how to compute the wavelength of WTMD's signal (89.7 MHz).  Note that MHz means 'million Hz."  Recall that radio waves travel at the speed of light.

8.  A C-note vibrates at 262 Hz (approximately).  Find the frequencies of the next 2 C's (1 and 2 octaves above this one).

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(answers)

1, 2.  See notes.

3.  200 m/s

4.  wavelength is 4 m.  Frequency is 6 Hz.

5.  3,000,000 / 340 --- that's around a million to one ratio

6.

a.  see notes

b.  frequencies are 10, 20 and 30 Hz, respectively, for n = 1, 2 and 3

c.  speeds are all constant

7.  speed of light divided by 89.7 MHz.  That is 300,000,000 / 89,700,000, which works out to around 3.3 m.

8.  524 Hz and 1048 Hz

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Wave questions II

Consider the musical note G, 392 Hz.  Find the following:

1.  The frequencies of the next two G's, one and two octaves above.

2.  The frequency of the G one octave lower than 392 Hz.

3.  The frequency of G#, one semi-tone (piano key or guitar fret) above this G.

4.  The frequency of A#, 3 semi-tones above G.

5.  The wavelength of the 392 Hz sound wave, assuming that the speed of sound is 340 m/s.

6.  What are the differences between longitudinal and transverse waves?  Gives examples of each.  What type of wave is sound?

7.  Here's a thought question for you - why does breathing in helium make your voice higher?

answers:

1.  392 x 2; 392 x 4

2.  392/2

3.  392 x 1.0594

4.  392 x 1.0594 x 1.0594 x 1.0594  (or 392 x 1.0594^3)

5.  340/392

6.  See notes.