SOLVE THESE PROBLEMS

RH = CH1 = CH2 = PHYS 251 TEST #5 5/2/22 Dr. Holmes NAME Key DO ALL EIGHT PROBLEMS. THE WORTH OF EACH PROBLEM IS MARKED BESIDE THE PROBLEM. SHOW YOUR WORK FOR PARTIAL CREDIT. 1. a) [4] The one-dimensional wave equation for a string is T azyraxz = m azyratz Where did this equation come from (that is, is it basic, or is it derived from more basic principles - and if so, what is that basic principle or principles)? b) [4] The one-dimensional wave equation for an electric eld wave in vacuum is azEyfaxz = |Joo aZEyraIZ. Where did this equation come from (that is, is it basic, or is it derived from more basic principles - and if so, what is that basic principle or principles)? c) [3] Where does mI'k = v = {(h'som) = c come from? d) [3] Ey(X,t) = Eosin(kx+mt) is a wave that moves in the [positive or negative] x direction? 2. a) What is the predicted speed for an electromagnetic wave in vacuum? [3] 3 x 108 mls b) Where does this value come from? (That is, what parameters of the vacuum does it depend on? [3] v = c = 'f[1f[8o [1] . c) If the electromagnetic wave were to travel in a transparent material different than vacuum, such as glass, would the wave travel slower, the same speed, or faster'? [2] slower . d) What would change in part b that would lead to your answer in part c? [3] an becomes a [where a=Ko, K is dielectric constant of material) . 3. Given that a one-dimensional wave can be described as a sine wave of amplitude 22 cm, frequency of 1,400 HZ, with a phase velocity of 175 m/s moving in the +x direction: a) What is the wavelength of this wave? [4] 0.125 m b) Write a function, y(x,t), for this wave: (be sure to have only x and t show up as variables; all other quantities should have values with units included) y(x,t) [4] 22 cm sin|[50. 3 rad/m] x [8,796 rams] t] c) If the frequency and physical medium did NOT change but the amplitude did change, would the following quantities change? Answer each with one of the following. [Yes would change; No: would not change:] wavelength phase velocity: power: [2] No [2] No [2] Yes . PHYS 251 Test #5 page 2 4. a) DESIGN a string (choose it's length, mass density, and tension) that when plucked will have a fundamental frequency of 440 HZ: [6] Length: Mass density: Tension: b) Based on your design, what is the phase velocity of waves on your string? [4] 5. a) Given that the intensity of a sound wave of frequency 1,400 Hz is 7.0 x 10-3 W/m?, what is the intensity in dB? [4] 98.5 dB b) Given that the intensity of a sound wave of frequency 400 Hz is 44 dB, what is the intensity in Watts/m2 ? (4] 2.51 x 10-8 W/m2 c) Does the frequency enter into calculations for part a only, for part b only, for both, or for neither? [2] neither d) If two waves with the two frequencies (1,400 Hz and 400 Hz) had the same power, would the lower frequency have a larger, the same, or smaller amplitude? [2] larger 6. a) Given that the intensity of a sound wave of frequency 1,400 Hz is 7.0 x 10-3 W/m? (same as in 5a above), what will its intensity be if the amplitude of the sound wave is increased by a factor of 4: (in Watts/m2)? (in dB)? [3] 1.12 x 10-1 W/m2 [1] 110.5 dB b) Given that the intensity of a sound wave of frequency 400 Hz is 44 dB (same as in 5b above), what will its intensity be if the amplitude stays the same but the frequency is increased by a factor of 10: (in Watts/m2)? (in dB)? [3] 2.51 x 10-6 W/m2 [1] _ 64 dB . c) Given that the intensity of a sound wave of frequency 1,400 Hz is 7.0x10-3 W/m2 (same as in 5a above) at a distance of 5 meters from the speaker, what will its intensity be at a distance of 25 meters from the speaker: (in W/m2)? (in dB)? [3] 2.80 x 104 W/m2 [1] 84.5 dBT. a) What is the speed of sound in air in a freezer if the temperature of the freezer is 40F ? [3] 305.6 mfs . b) What are the nominal lower and upper limits on the frequency of SOUND that are audible to the human ear at room temperature? Lower: upper: [2] 20 Hz [2] 20 000 Hz c) Does temperature affect the frequencies that the human ear can hear? (yeso): [1] No . d) What is the wavelength of the SOUND in the above freezer for the limits of audible sound: for the lower frequency ? for the upper frequency? [2] 15.3 m [2] .0153 m e) An FM radio station broadcasts its signal over an electromagnetic wave with a frequency of 91.1 MHZ. What is the wavelength for this electromagnetic wave? [2] 3.29 m f) An AM radio station broadcasts its signal over an electromagnetic wave with a frequency of 600 kHz. Is the wavelength for this wave longer, the same, or shorter than for the FM radio station of part e? [1] longer . 8 Consider a speaker that produces a sound of frequency 3,300 Hz. (In parts a and b, consider the air to be still - no wind, and consider the speed of sound in the air to be 340 mfs.) All answers for a, b, and c should be to the nearest Hz. a) Suppose that you are stationary and the speaker moves towards you at a speed of 22 m/s. What frequency will you now measure for the sound? [4] 3,523 Hz . b) Suppose that the speaker is held stationary, and you head away from the speaker at a speed of 33 mls. What frequency will you measure for the sound? [4] 2,930 Hz . c) Suppose that the speaker of frequency 3,300 Hz is mounted on a train that is leaving the station going North at 22 mls, you are approaching the station and the front of the train going South at a speed of 33 m/s, and there is an South wind (blowing from the South towards the North) at a speed of 15 m/s (relative to the station). What will you measure for the frequency of the sound [you must be precise: answer to the closest Hz]? [4] 3,345 Hz