Wave problems 1 and 2, with answers

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 0.25 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.  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.

6.  Middle C vibrates at 262 Hz (approximately).  Find the frequencies of the next 2 C's (1 and 2 octaves above this one).

Answers:

1/2.  See notes

3.  v = f l = 500(0.25) = 125 m/s

4.  wavelength (l) = 12/3 = 4 m

v = f l

24 = f (4)

f = 6 Hz

5.  v = f l

300,000,000 = (89,700,000) l

l = 300,000,000/89,700,000

6.  In music, octaves are found by doubling the frequency of the first note.

524 Hz, 1048 Hz

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.

answers:

1.  392 x 2 = 784 Hz; 392 x 4 = 1568 Hz

2.  392/2 = 196 Hz

3.  392 x 1.0594 = 415 Hz

4.  392 x 1.0594 x 1.0594 x 1.0594  (or 392 x 1.0594^3) = 466 Hz

5.  wavelength = speed / frequency = 340/392 = 0.87 m