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Suppose a flutist plays a 523-Hz C note with first harmonic displacement amplitude A1 = 100 nm. From Figure 17.21b read, by proportion, the displacement amplitudes of harmonics 2 through 7. Take these as the values, A2 through A7 in the Fourier analysis of the sound and assume
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- Item 9 Learning Goal: To learn the properties of logarithms and how to manipulate them when solving sound problems. The intensity of sound is the power of the sound waves divided by the area on which they are incident. Intensity is measured in watts per square meter, or W/m². The human ear can detect a remarkable range of sound intensities. The quietest sound that we can hear has an intensity of 10-¹2 W/m², and we begin to feel pain when the intensity reaches 1 W/m². Since the intensities that matter to people in everyday life cover a range of 12 orders of magnitude, intensities are usually converted to a logarithmic scale called the sound intensity level 3, which is measured in decibels (dB). For a given sound intensity I, B is found from the equation ß = (10 dB) log (1). where Io = 1.0 × 10-¹2 W/m². Part A What is the value of log(1,000,000)? Express your answer as an integer. ► View Available Hint(s) The logarithm of x, written log(x), tells you the power to which you would raise 10…arrow_forwardA wave is modeled by the wave function: y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)] 1. Find the wavelength, wave number, wave velocity, period and wave frequency. 2. Construct on the computer, in the same graph, the dependence of y (x, t) from x on t = 0 and t = 5 s in case the value of amplitude A corresponds to the first letter of your name: letter E A. A=0.1 mB. A=0.15 mC. A=0.2 mÇ. A=0.25 mD. A=0.3 mDh. A=0.35 mE. A=0.4 mË. A=0.45 mF. A=0.5 m G. A=0.55 mGj. A=0.6 mH. A=0.65 mI. A=0.7 mJ. A=0.75 mK. A=0.8 mL. A=0.85 mLl. A=0.9 mM. A=0.95 m N. A=1.05 mNj. A= 1.1 mO. A=1.15 mP. A=1.2 mQ. A=1.25 mR. A=1.3 mRr. A=1.35 mS. A=1.4 mSh. A=1.45 m T. A=1.5 mTh. A=1.55 mU. A=1.6 mV. A=1.65 mX. A=1.7 mXh. A=1.75 mY. A=1.8 mZ. A=1.85 mZh. A=1.9 m 3. After constructing the graph, make the appropriate interpretations and comments from the result that you got graphically. 4. How much is the wave displaced during the time interval from t = 0 to t = 5 s? Does it match this with the graph results?…arrow_forwardI got .28sin(19pix-13034pit) which is incorrectarrow_forward
- A wave is modeled by the wave function: y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)] 1. Find the wavelength, wave number, wave velocity, period and wave frequency. 2. Construct on the computer, in the same graph, the dependence of y (x, t) from x on t = 0 and t = 5 s and the amplitude is A= 1.3m 3. After constructing the graph, make the appropriate interpretations and comments from the result that you got graphically. 4. How much is the wave displaced during the time interval from t = 0 to t = 5 s? Does it match this with the graph results? Justify your answer. Is the material transported long wave displacement? If yes, how much material is transported over time interval from t = 0 to t = 5 s? Comment on your answer. We now consider two sound waves with different frequencies which have to the same amplitude. The wave functions of these waves are as follows: y1 (t) = A sin (2πf1t) y2 (t) = A sin (2πf2t) 5. Find the resultant wave function analytically. 6. Study how the resulting wave…arrow_forwardPlease use the equations provided to solve The speed of sound in a liquid or solid it’s much faster than the speed of sound in air, which is around 340 m/s. Write the equation Y(x,t)for a sound wave with the frequency and an amplitude given below. Show wavelength, wave number, period and natural frequency. Numbers in decimals not pi. Steel with a speed of 6956 m/s Assume frequency of 2013 Hz and amplitude of 18.3 dB.arrow_forwardsolve ASAParrow_forward
- a steel wire with a uniform tension T=600N, length L=2m and mass 8 kg. a) Find the elementary frequency of oscillation. b) if the maximum frequency that a person can hear is 10,000hz=f, what is the highest harmonic that this person can perceive?arrow_forwardA sinusoidall wave traveling in the positive x direction has an amplitude of 30.0 cm, a wavelength of 80.0 cm, and a frequency of 18.0 Hz. Find the angular frequency. O 103.5010 Hz O 100.5310 Gz O 100.5310 Hz O 105.3010 Hzarrow_forwardA sinusoidal wave has a displacement given by the formula 1. What is the Amplitude? 2. The Frequency is 3. The period is y = 30 Sin (40 Tit) Hz millisecondsarrow_forward
- Let us assume we are using SI units (kg, m, s). Consider the harmonic travelling wave 17 y(x, t) = = 12 cos(3x - 12πt). Assume the above harmonic wave is a solution of the motion of a string with tension T = 1 Newton. What is the string's density?p= kg/m What is its kinetic energy density? What is its kinetic energy over one wavelength? Ek What is its potential energy density? What is its potential energy over one wavelength? Ey = J/m J/marrow_forwardA tuning fork is held a certain distance from your ears and struck. Your eardrums’ vibrations after t seconds are given by p = 3 sin 2t. When a second tuning fork is struck, the formula p = 2sin(2t + π) describes the effects of the sound on the eardrums’ vibrations. The total vibrations are given by p = 3 sin 2t + 2 sin(2t + π). Solve, a. Simplify p to a single term containing the sine. b. If the amplitude of p is zero, no sound is heard. Based on your equation in part (a), does this occur with the two tuning forks in this exercise? Explain your answer.arrow_forwardConsider the surface density wave 01 = 010e (w+30-ar³/4) where t is time, the azimuthal angle, which increases clockwise, and r the radial coordi- nate. w is the angular frequency (w > 0), a is a positive constant. 10 is the amplitude of the wave. 01 1. Using mathematical arguments show whether the pattern described by σ₁ is rotating clockwise or anticlockwise. 2. Using mathematical arguments show whether the pattern described by σ is a trailing or a leading spiral.arrow_forward
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