Download Different Waves - Physics - Solved Paper and more Exams Physics in PDF only on Docsity! 1. Consider two waves on the same vibrating string. Which of the following statements are true: (a) two different waves might have different amplitudes, (b) two different waves might have different frequencies, (c) two different waves might have different wave speeds, (d) two different waves with the same frequency might have different wavelengths. The wave speed is the same for a given string ( /v F μ= , and we assume that the tension F is the same). The frequency and amplitude, however, are not properties of a string [remember, we are not talking about standing waves (fundamental modes) here]; rather, it is given by an “external agent” that drives the string. Thus, frequencies and amplitudes can be different, in contrast to v . (c) is not an option either: /v fλ = and if both v and f are the same, the wavelengths are the same too. (a) a, b (b) a, d (c) a, b, d (d) a, b, c, d (e) c, d 2. A 0.5-kg mass on a spring has its position as a function of time given by ( ) 0.03 sin 0.2 2 tx t m s π⎛= × −⎜ ⎝ ⎠ ⎞ ⎟ . Find the spring constant. ( ) ( )0sinx t A tω ϕ= + 1 0.2 k r m s ω = = ad 2 12.5 Nk m m ω= = (a) 2.5 N/m (b) 6.25 N/m (c) 12.5 N/m (d) 25 N/m (e) 50 N/m 3. A harmonic oscillator has angular frequency ω and amplitude A. What is the magnitude of the displacement when the elastic potential energy is equal to the kinetic energy? (Assume that the potential energy U=0 at equilibrium.) ( ) ( )cosx t A tω= ( ) ( ) 2 2 2 2 kx t mx t = ( ) ( ) 2 2 2 2 2cos sin 2 2 kA t m A tω ω ω = 2 k m ω = ( )2 1tg tω = 4 t πω = ± cos 4 2 Ax A π⎛ ⎞= =⎜ ⎟ ⎝ ⎠ (a) 0 (b) / 3A (c) / 2A (d) A (e) 2A 1 4. A transverse wave is propagated in a string stretched along the x-axis. The equation of the wave, in SI units, is given by: y = 0.005 cos [π (38t - 14x)]. The wave speed, including the sense of direction along the x-axis, in SI units, is closest to: ( ) ( ) (, cos cos 14 38 )y x t A kx t A x tω π= − = ⋅ − π ⋅ 38 2.7 14 v k ω π π = = ≈ (a) -3.7 (b) 2.7 (c) -2.7 (d) 0.37 (e) zero 5. A transverse wave is propagated in a string stretched along the x-axis. The equation of the wave, in SI units, is given by: y(x,t) = 0.6 cos[π (46t - 12x)]. The maximum speed of a particle on the string, in SI units, is closest to: ( ) ( ) ( ) ( ) (, cos 0.6cos 12 46 , 0.6 46 sin 12 46y x t A kx t x t y x t x tω π π π⎡ ⎤ ⎡= − = − + = − ⋅ − +⎣ ⎦ ⎣ )⎤⎦ Max ( )sin ... 1y → = max 0.6 46 86.7 /y m sπ= ⋅ ⋅ = (a) 27.6 m/s (b) 36.0 m/s (c) 55.2 m/s (d) 86.7 m/s (e) 112 m/s 6. The howler monkey is the loudest land animal and can be heard up to a distance of 8 km. Assume the acoustic output of a howler to be uniform in all directions. The distance at which the intensity level of a howler's call is 28 dB, in SI units, is closest to: ( ) ( ) 2 1 28 10 log I r dB dB I r = ⋅ ( ) ( ) 2 2 1 2 2 1 2 1( ) I r rI r r I r r ∝ = 2 1 1 2 2 2 28 10 log 20 logr rdB dB dB r r = ⋅ = 3 1 2 28/20 1.4 8 10 320 10 10 r mr m⋅= = = (a) 320 m (b) 480 m (c) 630 m (d) 980 m (e) 1250 m 7. After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 0.5 m. She finds that the pendulum makes 100 complete swings in a time of 135 s. What is the value of the acceleration due to gravity at the planet’s surface? 2
