Solutions to homework problem set #1

Text pages 25 and 26, problems P3, P11, P15, PM2, PM10

P3. We know that light travels through a vacuum because light from the sun and the stars reaches us. While this is a true statement, it does not absolutely prove the point, since space might be filled with some material that we can’t see. In fact, in the last years of the 19^th century, physicists postulated the existence of an invisible “ether” whose primary purpose was to act as the medium for the transport of light and other electromagnetic waves.

P11. The wavelength is the distance between consecutive points with the same displacement. For example, between two maxima or two minima. The wavelength in the figure is about 3.5 cm.

P15. The frequency is defined as the number of cycles per second, although the medical profession tends to report pulses rates in beats per minute rather than beats per second. A typical value is about 60 or 70 beats per minute, which you could measure by counting the number of pulses at your wrist for one minute. You could also count for a fraction of a minute and scale the answer by the appropriate factor. For example, you might count for 15 seconds and multiply the answer by 4. To convert to frequency units, you should divide the pulse rate per minute by 60. Thus 60 beats per minute is 1 beat per second or a frequency of 1 Hz; 70 beats per minute would be a frequency of 70/60 or about 1.167 Hz.

PM2. If the pulse requires 2.5 seconds to make the round trip, then it reaches the moon in one half of that time or 1.25 seconds. Since the velocity of light is 3 x 10⁸ m/s, the distance to the moon is 1.25 x 3 x 10⁸ m = 3.75 x 10⁸ m = 3.75 x 10⁵ km.

PM15. The frequency is the velocity of propagation of light divided by the wavelength, which is given in the problem. Thus:

n = 3 x 10⁸/575 x 10^-9 = 5.22 x 10¹⁴ Hz = 522 THz

Note that it is important to convert the values in the numerator (the speed of light) and denominator (the wavelength) to meters.

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