Word Problems: Remember to use GRASP and show string number before stating final answer. 1) Abobon the end of a spring is pulled down and released. If the bob moves up and down 12 times in 3.6 seconds, determine the period and frequency of the oscillation [Ans: 0.30s;3.3Hz] 2) A piston in a car moves up a down 150 times per minute (150 rpm)Find the frequency in Hz and the period of the vibration. [Ans: 2.5Hz;0.40s] 3) The frequency of a note produced by a tuning fork is 440 Hz. Find the wavelength of the sound given a sound speed of (a) 332m/s (b) 344m/s. [Ans: 0.755 m 0.782 m] 4) The frequency of another tuning fork is 512 Hz. If the wavelength of the vibration is 66.4 cm, find the speed of sound (Ans: 3.40times 10^2m/s) 5) Determine the speed of a wave with a frequency of 1025 MHz and a wavelength of 2.9 m (Ans: 3.0times 10^8m/s]

## Word Problem Solutions:<br /><br />**1) Oscillating Bob**<br /><br />* **Given:** 12 oscillations in 3.6 seconds<br />* **Required:** Period (T) and Frequency (f)<br />* **Relationship:** f = 1/T and T = 1/f<br /><br />* **Solution:**<br /> * T = Total time / Number of oscillations<br /> * T = 3.6 s / 12 oscillations<br /> * T = 0.30 s <br /> * f = 1 / T<br /> * f = 1 / 0.30 s<br /> * f = 3.3 Hz<br /><br />* **Answer 1:** Period (T) = 0.30 s; Frequency (f) = 3.3 Hz<br /><br /><br />**2) Car Piston**<br /><br />* **Given:** 150 oscillations per minute (rpm)<br />* **Required:** Frequency (f) in Hz and Period (T)<br />* **Relationship:** f = oscillations/time and T = 1/f<br /><br />* **Solution:**<br /> * Convert rpm to Hz:<br /> * f = 150 oscillations / 60 seconds<br /> * f = 2.5 Hz<br /> * T = 1/f<br /> * T = 1 / 2.5 Hz<br /> * T = 0.40 s<br /><br />* **Answer 2:** Frequency (f) = 2.5 Hz; Period (T) = 0.40 s<br /><br /><br />**3) Tuning Fork (440 Hz)**<br /><br />* **Given:** Frequency (f) = 440 Hz; Speed of sound (v) = (a) 332 m/s, (b) 344 m/s<br />* **Required:** Wavelength (λ)<br />* **Relationship:** v = fλ<br /><br />* **Solution (a):**<br /> * λ = v / f<br /> * λ = 332 m/s / 440 Hz<br /> * λ = 0.755 m<br /><br />* **Solution (b):**<br /> * λ = v / f<br /> * λ = 344 m/s / 440 Hz<br /> * λ = 0.782 m<br /><br />* **Answer 3:** Wavelength (λ) = (a) 0.755 m; (b) 0.782 m<br /><br /><br />**4) Tuning Fork (512 Hz)**<br /><br />* **Given:** Frequency (f) = 512 Hz; Wavelength (λ) = 66.4 cm = 0.664 m<br />* **Required:** Speed of sound (v)<br />* **Relationship:** v = fλ<br /><br />* **Solution:**<br /> * v = fλ<br /> * v = 512 Hz * 0.664 m<br /> * v = 340 m/s<br /><br />* **Answer 4:** Speed of sound (v) = 3.40 x 10² m/s<br /><br /><br />**5) Wave Speed**<br /><br />* **Given:** Frequency (f) = 1025 MHz = 1.025 x 10⁹ Hz; Wavelength (λ) = 2.9 m<br />* **Required:** Speed of wave (v)<br />* **Relationship:** v = fλ<br /><br />* **Solution:**<br /> * v = fλ<br /> * v = (1.025 x 10⁹ Hz) * 2.9 m<br /> * v = 2.97 x 10⁹ m/s (approximately 3.0 x 10⁸ m/s given potential rounding in the problem)<br /><br />* **Answer 5:** Speed of wave (v) = 3.0 x 10⁸ m/s (approximated)<br />