Similarly, the repeat time-or period, 7-of a wave is the time required for one wavelength to pass a given point, as illustrated in Figure 14-7. Closely related to the period of a wave is its frequency, /, which, as with oscillations, is defined as the inverse of the period: / = 1/T. Combining these observations, we see that a wave travels a distance A in the time T. If we apply the definition of speed-distance divided by time-it follows that the speed of a wave is: Speed of a Wave distance A - Af 14-1 time SI unit: m/s This result applies to all waves. EXERCISE 14-1 FREQUENCY AND WAVELENGTH Sound waves travel in air with a speed of 343 m/s. (a) Middle C on a piano produces sound waves with a wavelength of 1.31 m. What is the frequency of middle C? (b) Dogs can hear sounds with frequencies as high as 45,000 Hz. What is the wavelength of such sounds? REASONING AND SOLUTION Wave speed, wavelength, and frequency are related by e - Af. This relationship can be rearranged to solve for any one quantity in terms of the other two. (a) Wesolve s - Af for the frequency, and then substitute e - 343 m/sand A = 1.31 m: 343 m/'s f - A 1.31 m - 262 Hz (b) We solve e - Af for the wavelength, and then substitute e - 343 m/s and / - 45,000 Hz: 343 m/'s A - 7.62 mm 45,000 HzQuestion 5 (1 point) Retake question A surfer floating beyond the breakers notes 19 waves per minute passing her position. If the wavelength of these waves is 36.6 m, what is their speed, in meters per second? Use the definition of period (or frequency) from the beginning of section 13-1. Convert 19 waves per minute to waves per second. Then use Eq. 14-1 to calculate the speed