Chapter 15 - Mechanical Waves - Problems - Exercises - Page 497: 15.2

(a) The distance between the red dots is 17.2 m. The distance between the blue dots is 1.72 cm. (b) The blue dots would be too close together to measure with a meter stick. The red dots would be too far apart to measure with a meter stick. (c) The distance between the red dots is 74 m. The distance between the blue dots is 7.4 cm. The blue dots would be too close together to measure with a meter stick. The red dots would be too far apart to measure with a meter stick.

(a) We can find the distance between the red dots, which is the wavelength of the wave with a frequency of 20.0 Hz. $\lambda~f = v$ $\lambda = \frac{v}{f}$ $\lambda = \frac{344~m/s}{20.0~Hz}$ $\lambda = 17.2~m$ The distance between the red dots is 17.2 m. We can find the distance between the blue dots, which is the wavelength of the wave with a frequency of 20.0 kHz. $\lambda~f = v$ $\lambda = \frac{v}{f}$ $\lambda = \frac{344~m/s}{20.0~kHz}$ $\lambda = 0.0172~m = 1.72~cm$ The distance between the blue dots is 1.72 cm. (b) The blue dots would be too close together to measure with a meter stick. The red dots would be too far apart to measure with a meter stick. (c) We can find the distance between the red dots, which is the wavelength of the wave with a frequency of 20.0 Hz. $\lambda~f = v$ $\lambda = \frac{v}{f}$ $\lambda = \frac{1480~m/s}{20.0~Hz}$ $\lambda = 74~m$ The distance between the red dots is 74 m. We can find the distance between the blue dots, which is the wavelength of the wave with a frequency of 20.0 kHz. $\lambda~f = v$ $\lambda = \frac{v}{f}$ $\lambda = \frac{1480~m/s}{20.0~kHz}$ $\lambda = 0.074~m = 7.4~cm$ The distance between the blue dots is 7.4 cm. The blue dots would be too close together to measure with a meter stick. The red dots would be too far apart to measure with a meter stick.